how do we write repeated multiplication as powers and how do we evaluate powers

Answers

Answer 1

Answer:

[tex]5 { \\ }^{2} [/tex]

Step-by-step explanation:

exponents are ways to write multiplication powers 5

[tex]5 {}^{2} [/tex]

= 5×5 = 25

Answer 2

Answer:

the exponent signifies the number of times the base is a factorpowers can be evaluated by performing the multiplications

Step-by-step explanation:

You want to know how multiplication and powers are related, and how powers can be evaluated.

Repeated addition

You may be familiar with the fact that a coefficient is used to signify repeated addition:

  y + y + y + y = 4y

The coefficient of 4 in 4y signifies that y is in the sum that many times.

Repeated multiplication

An exponent is used to signify repeated multiplication:

  y × y × y × y = y⁴ . . . . y to the fourth power

The exponent of 4 signifies that y is a factor in the product that many times.

In typeset text, the exponent is rendered in a superscript font. In plain text, the exponent (power) is identified using a caret (^):

  y⁴ = y^4

Rules of exponents

The rules of exponents derive from the idea of exponents signifying repeated multiplication:

  [tex](x\cdot x)=x^2\\(x\cdot x\cdot x)=x^3\\(x\cdot x)\cdot(x\cdot x\cdot x)=(x\cdot x\cdot x\cdot x\cdot x)\ \Longrightarrow\ x^2\cdot x^3=x^{2+3}=x^5[/tex]

Division has a similar rule.

  [tex]\dfrac{(x\cdot x\cdot x\cdot x\cdot x)}{(x\cdot x)}=(x\cdot x\cdot x)\ \Longrightarrow\ \dfrac{x^5}{x^2}=x^{5-2}=x^3[/tex]

This supports the idea that a positive exponent in the denominator is the same as a negative exponent in the numerator, and vice versa.

Evaluating powers

Powers can be evaluated in a straightforward way by carrying out the multiplications.

In general, the number of significant digits in the result will be the product of the exponent and the number of significant digits in the base.

For example, 9.2^5 could be expected to have 2×5 = 10 significant digits:

  9.2^5 = 9.2×9.2×9.2×9.2×9.2 = 65,908.15232

Most calculators are limited to 12 digits or less, and most spreadsheets are limited to 16 digits or less. Some special-purpose calculators have "variable" precision, so are able to properly render higher powers of numbers with more than 1 or 2 significant digits.

A calculator may use any of several techniques for evaluating powers. Among them might be ...

logarithmsrepeated squaring.

Logarithms

Logarithms turn a power problem into a multiplication problem:

  log(9.2^5) = 5·log(9.2)

Of course, once the logarithm is found, the issue of evaluating powers comes back:

  9.2^5 = 10^(5×log(9.2)) ≈ 10^(4.818939136727776)

Fortunately, there are methods of evaluating antilogs that simplify this part of raising to a power. The difficulty is that precision may be lost. Here, using the rounded value 10^(4.81893913673) gives the result 65,908.152320337..., which is in error after the 10th digit.

Repeated squaring

An integer power can be written as a sum of powers of 2. For example, ...

  37 = 32 +4 +1 = (8 +1)4 +1

Then ...

  9.2^37 = (((((9.2^2)^2)^2 · 9.2)^2)^2) · 9.2

This requires only 7 multiplications, not 36

__

Additional comment

Only the first token after the caret is considered to be the exponent:

  y^4x = (y^4)(x) . . . . . the first token is 4

  y^1/2 = (y^1)/2 = y/2 . . . . the first token is 1

If the exponent has multiple parts, they should be enclosed in parentheses:

  [tex]y^{3x+1}[/tex]

will be written in plain text as ...

  y^(3x+1)

and ...

  y^(1/2) = √y

You also need to be careful writing multiple exponents using the caret symbol. Parentheses are usually required. The Order of Operations has you evaluate multiple exponents right to left.

  3^4^5 = 3^(4^5) = 3^1024

  (3^4)^5 = 3^20


Related Questions

25 pts - 37.5 if brainliest
Find the equation of the trend line (line of best fit)

Answers

Based on the given points on the graph, the equation for the line of best fit or the trend line is y = 1.874x + 3.656

What is the trend line?

Due to the fact that the points on the graph are not on a straight line, the least squares method can be used to find the line of best fit equation.

Using a linear regression calculator, you can find the equation of the trend line by inputting the values of y and x in the graph.

When run through a linear regression calculator, the result will be:

y = 1.874x + 3.656

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On January 1, Year 1, Jana started a small flower merchandising business that she named Jana’s Flowers. The company experienced the following events during the first year of operation: Started the business by issuing common stock for $43,000 cash. Paid $28,000 cash to purchase inventory. Sold merchandise that cost $20,000 for $42,000 on account. Collected $37,000 cash from accounts receivable. Paid $9,800 for operating expenses. Required a. Organize ledger accounts under an accounting equation and record the events in the accounts. In the last column of the table, provide appropriate account titles for the Retained Earnings amounts. b-1. Prepare an income statement. b-2. Prepare a balance sheet. b-3. Prepare a statement of cash flows. c. Since Jana sold inventory for $42,000, she will be able to recover more than half of the $43,000 she invested in the stock. Do you agree with this statement?

Answers

a) The organization of ledger accounts under an accounting equation and journal entries are as follows:

Accounting Equation:

                         Assets                               =  Liabilities + Equity

            Cash +   Inventory + A/Receivable                    C.Stock  R/Earnings

1.       $43,000                                                                 $43,000

2.       -28,000   $28,000

3.                                                $42,000                                          42,000 S/Revenue

4.                        -20,000                                                                  -20,000 COGS

5.        37,000                            -37,000

6.        -9,800                                                                                     -9,800 Op Exp.

Bal. $42,200      $8,000           $5,000                      $43,000    $12,200

Journal Entries:

Debit Cash $43,000

Credit Common Stock $43,000

Debit Inventory $28,000

Credit Cash $28,000

Debit Accounts Receivable $42,000

Credit Sales Revenue $42,000

Debit Cost of goods sold $20,000

Credit Inventory $20,000

Debit Cash $37,000

Credit Accounts Receivable $37,000

Debit Operating expenses $9,800

Credit Cash $9,800

b1)

Jana's Flowers

Income Statement

For the year ended December 31, Year 1

Sales Revenue           $42,000

Cost of goods sold    $20,000

Gross profit                $22,000

Operating expenses   $9,800

Net income                $12,200

b2) Jana's Flowers

Balance Sheet

December 31, Year 1

Cash                           $42,200

Accounts Receivable  $5,000

Inventory                     $8,000

Total assets             $55,200

Common Stock        $43,000

Retained Earnings      12,200

Total equity            $55,200

b3) Jana's Flowers

Statement of Cash Flows

For the year ended December 31, Year 1

Net income                $12,200

Changes in working capital:

Accounts Receivable  (5,000)

Inventory                      (8,000)

Operating cash flow     ($800)

Financing activities:

Common Stock       $43,000

Cash flows              $42,200

c) I do not agree with this statement.  It does not necessarily flow that Jana selling $42,000 in goods will be able to recover more than half of the $43,000 she invested in her business.  So far, she has made $12,200 from her investment.

Data Analysis:

Cash $43,000 Common Stock $43,000

Inventory $28,000 cash $28,000

Accounts Receivable $42,000 Sales Revenue $42,000

Cost of goods sold $20,000 Inventory $20,000

Cash $37,000 Accounts Receivable $37,000

Operating expenses $9,800 Cash $9,800

Thus, it will take time for Jana to recover her investment in the business.

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A 61 in. wood plank is cut into 3 pieces. The longest piece is 5 times the length of the smallest piece. The medium piece
less than 2 times the length of the smallest.
1. If z represents the length of the smallest piece, write the expression that represents the medium size piece.
2. Write an equation to show that length of all the pieces together equal to the total length of 61 inches.
3. What is the length of each piece of wood? Explain how you know you are correct.

Answers

The length of the smallest, medium and the longest piece of wood are 7.625, 15.25 and 38.125 inches.

How to represent expressions?

The wood is 61 inches and it is divide into 3 pieces.

The longest piece is 5 times the length of the smallest piece.

The medium piece less than 2 times the length of the smallest.

let

z = length of the smallest piece of wood

longest piece = 5z

medium piece = 2z

The equation to represent the total piece together is equal to 61 inches.

z + 5z + 2z = 61

Therefore, the length of each wood piece can be calculated as follows:

z + 5z + 2z = 61

8z = 61

z = 61 / 8

z = 7.625 inches

longest piece = 5(7.625) = 38.125 inches

medium piece = 2(7.625) = 15.25 inches

Therefore, the length of the smallest, medium and the longest piece of wood are 7.625, 15.25 and 38.125 inches.

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greatest common factor of 2a and 4ab

Answers

Answer: GCF: 2a

Step-by-step explanation:

In order to find the factors, we need to list the prime factorization of 2a and 4ab, assuming a and b are prime numbers.

2a: 2*a

4ab: 2*2*a*b

Notice any common factors?

GCF: 2*a=2a

GCF: 2a

-x = 7x -56
pls i need anwer

Answers

-x = 7x-56
-8x = -56
x=7

Public school per-student expenditures increased approximately linearly from $4.6 thousand in 1990 to $10.8 thousand in 2013. Predict the per-student expenditure in 2024.
In 2024 public school per-student expenditures will be about $thousand.
(Round the final answer to two decimal places as needed. Round all intermediate values to two decimal places as needed.

Answers

per-student expenditures will be about $ 9.16.

Public school per-student expenditures in 1990 is $4.60

per-student expenditures in 2013 is $10.8

in 23 years per student expenditure has increase of 10.8-4.60 = $6.2

in 1 years per student expenditure has increase of  $6.2/23.

in 34 years per student expenditure has increase of  ($6.2/23)34 =$9.16

per-student expenditures will be about $ 9.16.

the act of spending (as money, time, or power) 2 : something this is spent hold a file of your costs. expenditure.

What are examples of costs?

Expenditure – this is the whole purchase fee of a great or service. for instance, a agency buys a $10 million piece of device that it estimates to have a useful life of five years. this will be labeled as a $10 million capital expenditure.

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what is the range of d

Answers

Answer:

A

Step-by-step explanation:

Range is on the y-axis, therefore, it would be from -1 to 5.

The range is the y -axis

find the area of the circle

Answers

Answer:

113.04 square feet

Step-by-step explanation:

A = π[tex]r^{2}[/tex]

A = π [tex](6[/tex][tex])^{2}[/tex]

A = 3.14 (36)

A = 113.04

Me deben el 20% de 18700 y me pagan el 15% de 900 cuánto me deben aún?

Answers

Answer:

3

Step-by-step explanation:

certain grocery store charges a fee of 3% of the total bill to have groceries delivered. What is the total price the store charges to deliver $140 worth of groceries?

Answers

The total price the store charges to deliver $140 worth of groceries will be $4.20.

How to calculate the percentage?

It should be noted that the certain grocery store charges a fee of 3% of the total bill to have groceries delivered.

Therefore, the total price the store charges to deliver $140 worth of groceries will be:

= Percentage charged × Cost

= 3% × $140

= 0.03 × $140

= $4.20

The amount charged is $4.20.

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What is the answer to Simplify 2x³ x 5x²

Answers

Answer:

Your answer is [tex]2x^{10}[/tex].

Step-by-step explanation:

Find the sum: 1.23 + 4.99.

Answers

Answer: 4.113

Step-by-step explanation: so like 1 goes into 4 4 times and then 2 dont go inna 9 so you got 11 because if you cant go down u goin up and then  da three go into nine evenly so like i hope you fail

Answer:

6.22

Step-by-step explanation:

1.23 + 4.99 is equal to 6.22.

(If adding decimals is a harder concept for you, just ignore the decimal point and add normally.)

Hope this helped!

(ratings and voting brainliest always help)

Write 53/16 as a decimal.​

Answers

Answer:

3.3125

Step-by-step explanation:

53/16  is the same as   53 ÷ 16 =3.3125

What is the decimal equivalent of each rational number? a. ___9/11 b. __4/5 c. ___-17/5 d. __5/9

Answers

i’m not positive im right but 1. complex fraction 2. terminating decimal 3. additive inverse

Please, I will mark brainliest.

Answers

Answer: RS=2.4

Step-by-step explanation:

QR=RS  ==> R is the midpoint of QS, so the distance from point R and point Q is equal to the distance from point R and point S.

7x-6=2x

7x=2x+6

5x=6

x=6/5

x=1.2

RS=2x

RS=2(1.2)

RS=2.4

how to increase the accuracy of simpson rule and maclaurin series expansion respectively? ​

Answers

Because it matches a parabola to the curve rather than a straight line, Simpson's rule is more precise.

The other approaches are only accurate for functions whose graphs are linear, whereas Simpson's rule yields the exact area beneath the graphs of functions of degree two or less (parabolas and straight lines).

Why is trapezoidal less accurate than Simpson's rule?

When the underlying function is smooth, Simpson's Rule is more accurate than the trapezoidal rule because it employs quadratic approximations rather than linear ones. In cases where there are an odd number of evenly spaced points, the formula is typically provided.

What are Simpson's rule's restrictions?

It is obviously incorrect because the actual integral will always differ from it (except in some cases, such as the area under straight lines). Integrals, unlike Simpson's technique, allow you to obtain precise results in terms of basic constants.

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20 10 12 13 4 1 5 0 19
Place for min , med, mode etc

Answers

0,1,4,5,13,14,10,15,19

square root of 72/98​

Answers

Answer:√78= 8.9 √98= 9.9

Step-by-step explanation:

Answer:

6/7

Step-by-step explanation:

So first, we can simplify 72/98. If we divide both the numerator and denominator by 2, to get a simplified fraction.  So we need to solve 72/2 and 98/2.  72/2 = 36 and 98/2 = 49 So now we have a simplified fraction. So now, we are left with the square root of 36/49, and we apply the radical rule. So now we have simplified radicals that make things easier. The square root of 36 is 6, while the square root of 49 is 7. This is because 36 can be broken down into factors of 6 and 6, so like 6^2 = 36. So square root of 36 is 6. While 49 can be broken down as 7 and 7, so like 7^2 = 49, so square root of 49 is 7. Therefore our answer is 6/7.

I hope this helps, have a blessed day!

Write 0.0000629 in scientific notation

Answers

Answer:

6.29 × 10^-5

Step-by-step explanation:

0.0000629

The number part of the answer is 6.29

To go from 0.0000629 to 6.29, the decimal point needs to move 5 places to the right, so the exponent on the 10 must be -5.

0.0000629 = 6.29 × 10^-5

Answer: 6.29*10^(-5)

Step-by-step explanation:

0.0000629=

0.629*10^(-4)=      ==> there are 4 zeros before the decimal point.

6.29*10^(-(4+1))=6.29*10^(-5)

Question 9 of 20
The police department of a city with a population of 150,000 wants to know
how many residents wear their seatbelts regularly. Which sample size would
make the study most reliable?
OA 150
OB. 1500
OC.5
D. 15

Answers

The sample size that would make the study on the residents that wear seatbelts regularly most reliable is B. 1,500.

Which sample size is more reliable?

When creating samples, there is a general rule that the higher the sample size, the more reliable the study is.

This is because a larger sample size is more likely to capture the characteristics of the population it is based on.

The most reliable sample size here is therefore 1,500 people.

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14. The maximum capacity for seating in a theater is 500 people. The theater sells two types of tickets, adult tickets for $7.25 each and child tickets for $4 each. If they sold out on a certain showtime and made a total of $3,157 in ticket sales, how many of each types of tickets was sold out that showtime?

Answers

Step-by-step explanation:

set x as the number of the adults in the show

500-x - number of children

(500-x)×4+7.25x=3157

2000-4x+7.25x=3157

3.25x=1157

3×1/4x=1157

13/4x=1157/×4

13x=4628/÷13

x=356

356 adult tickets was sold out.

500-356=144

144 child tickets was sold out.

Answer:

Adult tickets sold = 356

Child tickets sold = 144

Step-by-step explanation:

Given information:

Maximum number of seats = 500Cost of adult ticket = $7.25Cost of child ticket = $4Total revenue of sold-out show = $3,157

Define the variables:

Let x = the number of adult tickets sold.Let y = the number of child tickets sold.

Create two equations from the given information:

[tex]\textsf{Equation 1}: \quad x + y = 500[/tex]

[tex]\textsf{Equation 2}: \quad 7.25x+4y=3157[/tex]

Rewrite Equation 1 to make y the subject:

[tex]\implies y=500-x[/tex]

Substitute this into Equation 2 and solve for x:

[tex]\implies 7.25x+4(500-x)=3157[/tex]

[tex]\implies 7.25x+2000-4x=3157[/tex]

[tex]\implies 3.25x+2000=3157[/tex]

[tex]\implies 3.25x=1157[/tex]

[tex]\implies x=356[/tex]

Substitute the found value of x into the rewritten form of Equation 1 and solve for y:

[tex]\implies y=500-356[/tex]

[tex]\implies y=144[/tex]

Solution

Adult tickets sold = 356Child tickets sold = 144

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Han ran 1/4 the length of his road,which is 7 miles long how far did han run?

Answers

Han ran 1.75 miles

because 25% of 7 is 1.75

I need help with 19 please. I will give Brainly and bunch of extra points. Thank you .

Answers

Hope this makes sense

write a problem based on the information given c = regular cost of one airline ticket 0.2c = amount of 20% promotional discount 3(c - 0.2c) = 330​

Answers

The question for this information:

The cost of buying 3 airline tickets at a promotional discount of 20% is 330 dollars. Find the regular cost of 1 ticket.

Discounts and allowances are price reductions from a product's or service's base price.

Discount is calculated by subtracting the sell price of an article from its Marked price.

The given conditions in the question are

C=regular cost of a ticketamount of promotional discount=20%=0.2cAnd the expression 3(c - 0.2c) = 330​

So from the above information we can see that if the price of a ticket is c dollars then the discounted price of 1 ticket will be (c - 0.2c).

Total price of 3 tickets =3(c - 0.2c)

but the total price is 330 dollars

Therefore:

3(c - 0.2c) =330

or, 2.4c=330

or, c=330÷2.4

or, c=137.5 dollars

Hence the regular price of each ticket is 137.50 dollars.

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What is the standard unit of temperature? What can be used to measure temperature?

Answers

Answer:

Kelvin, thermometer

Step-by-step explanation:

Unit: kelvin

Measure temperature: thermometer

Classify each of the following statements as true or false. If false, tell why. a. 5 is a divisor of 20. b. 10 is a multiple of 20.​

Answers

Answer:

Yes; no

Step-by-step explanation:

a. If we divide 20 by 5, we get 4. Meaning, both 4 and 5 are divisors of 20.

b. 10 is not a multiple of 20; The multiples of 20 are 20, 40, 60, 80, 100, 120, 140, etc. Multiples only go upwards not down. Nothing plus 20 is equal to 10 therefore 10 is not a multiple of 20. 20 is a multiple of 10 though.

How is it similar and how is it different?

Answers

Using the intersection operation between two data-sets, it is found that the graph of x > a and x < b is similar to the graph of x > a for a < x < b and different for x > b.

What is the result of the intersection operation between two data-set?

The result of the intersection operation between two data-set is the set that contains elements that belong to both sets.

For this problem, we have that a is to the left of b, as a < b, hence:

a is plotted before b on the number line.The intersection between the operations x > a and x < b is the following interval: a < x < b.

Hence:

The graph of x > a and x < b is similar to the graph of x > a for a < x < b and different for x > b.

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how to do universal math by hands

Answers

Answer:

find the profound of life by your ethernal soul

Which of the following are solutions to the quadratic equation below? Check all that apply. X^2+16=2

Answers

Step-by-step explanation:

x²+16=2

x²+16-2=0

x²+14=0

x²=-14

x=√-14=7i

There are 15 triangles and 6 circles. What is the simplest ratio of circles to triangles?

Answers

Answer:

2:5, 2/5, 2 to 5

Step-by-step explanation:

The ratio is 6 to 15, but you can simplify that to 2 to 5.

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