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Algebra II : Multiplying and Dividing Exponents

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #3624 : Algebra Ii

Divide: $\frac{8^{-3}}{2^{-3}}$

Possible Answers:

$\frac{1}{32}$

$\frac{1}{4}$

$\frac{1}{2096}$

$\frac{1}{4096}$

$\frac{1}{64}$

Correct answer:

$\frac{1}{64}$

Explanation:

To be able to subtract the exponents, we will need to have similar bases.

Convert the numerator to base two.

$\frac{8^{-3}}{2^{-3}} = \frac{2^{3(-3)}}{2^{-3}}= \frac{2^{-9}}{2^{-3}}$

The expression becomes:

$2^{-9-(-3)} = 2^{-6}= \frac{1}{2^6} = \frac{1}{64}$

The answer is: $\frac{1}{64}$

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Example Question #3625 : Algebra Ii

Divide: $\frac{4^{22}}{16^{-5}}$

Possible Answers:

$\frac{1}{4^{17}}$

$4^{12}$

$4^{32}$

$\frac{1}{4^{27}}$

$2^{12}$

Correct answer:

$4^{32}$

Explanation:

In order to be able to simplify the exponents by subtraction, we will need to rewrite the denominator with a common base. Rewrite the number 16 as base 4.

$\frac{4^{22}}{16^{-5}} = \frac{4^{22}}{4^{2(-5)}} = \frac{4^{22}}{4^{-10}}$

Now that we have common bases, we can subtract the exponents since the bases of a power are divided.

$4^{22-(-10)} = 4^{32}$

The answer is: $4^{32}$

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Example Question #3626 : Algebra Ii

Divide the exponents: $\frac{x^{-6}}{x^3}\div x^4$

Possible Answers:

$\frac{1}{x}$

$\frac{1}{x^5}$

$\frac{1}{x^7}$

$\frac{1}{x^8}$

$\frac{1}{x^{13}}$

Correct answer:

$\frac{1}{x^{13}}$

Explanation:

Evaluate the first term by subtracting the exponents. This is allowed since the bases are common.

$\frac{x^{-6}}{x^3} = x^{-6-3}=x^{-9}$

Divide this term with the second term.

$x^{-9}\div x^4 = \frac{x^{-9}}{x^4}$

Repeat the process.

$x^{-9-4} = x^{-13} = \frac{1}{x^{13}}$

The answer is: $\frac{1}{x^{13}}$

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Example Question #3627 : Algebra Ii

Divide: $\frac{3^{12}}{27^{36}}$

Possible Answers:

$\frac{1}{3^9}$

$\frac{1}{3^{96}}$

$\frac{1}{3^{27}}$

$3^{96}$

$\frac{1}{9^3}$

Correct answer:

$\frac{1}{3^{96}}$

Explanation:

Convert the base of the denominator to base three in order to match the numerator.

$\frac{3^{12}}{27^{36}} =\frac{3^{12}}{3^{3(36)}}$

Multiply the exponents on the bottom.

$\frac{3^{12}}{3^{108}}$

Subtract the exponents.

$\frac{3^{12}}{3^{108}} = 3^{12-108} = 3^{-96}$

We can rewrite this as a fraction based on the following rule.

$x^{-n} = \frac{1}{x^n}$

$3^{-96} =\frac{1}{3^{96}}$

The answer is: $\frac{1}{3^{96}}$

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Example Question #161 : Simplifying Exponents

Simplify $x^3x^{-4}x^7$

Possible Answers:

x^14

x^6

x^1

x^7

Correct answer:

x^6

Explanation:

Combine all like variables. We only have the variable 'x', so we can skip that step. to multiply or divide exponents, you add, so you get 3 + (-4) + 7 = 6. The answer is x^6

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Example Question #162 : Simplifying Exponents

Simplify $\frac{x^6x^2}{x^4x^3}$

Possible Answers:

x^3/x^2

$x^{-2}$

x^3

Correct answer:

Explanation:

Combine all like variables. We only have the variable 'x', so we can skip that step. Simplify the numerator and denominator. This gives you $\frac{x^8}{x^7}$ . Simplifying this further gives you .

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Example Question #163 : Simplifying Exponents

Simplify $x^3x^{-23}x^2$

Possible Answers:

$\frac{1}{x^{28}}$

$x^{18}$

$\frac{1}{x^{18}}$

$x^{28}$

Correct answer:

$\frac{1}{x^{18}}$

Explanation:

First combine like variables. There is only one variable in this equation, so you can skip that step. Next add exponents when they are being multiplied. 3+(-23)+5=-18 which would be equal to $\frac{1}{x^{18}}$

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Example Question #164 : Simplifying Exponents

Simplify $\frac{x^{-15}}{x^{-22}}$

Possible Answers:

x^7

x^2

$\frac{1}{x^4}$

$x^{-7}$

Correct answer:

x^7

Explanation:

First combine like variables. There is only one variable in this equation, so you can skip that step. Next, move negative exponents to the other side of the fraction to get $\frac{x^{22}}{x^{15}}$ . Finally simplifying gives x^7

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Example Question #165 : Simplifying Exponents

Simplify $x^{-16}x^4x^{12}$

Possible Answers:

1/x

x^2

Correct answer:

Explanation:

First combine like variables. There is only one variable in this equation, so you can skip that step. Next, you add the exponents because we are multiplying. -16+4+12=0. x^0=1

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Example Question #163 : Multiplying And Dividing Exponents

Simplify $\frac{x^{-3}x^{4}x^{-5}}{x^{-5}}$

Possible Answers:

$x^{-16}$

$x^{-1}$

$x^{16}$

Correct answer:

Explanation:

First combine like variables. There is only one variable in this equation, so you can skip that step. Next, you move negative exponents to the opposite side of the fraction and then add the exponents because we are multiplying. 4+5=9 and 3+5=8 giving us $\frac{x^9}{x^8}$ which simplifies to .

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Algebra II : Multiplying and Dividing Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #3624 : Algebra Ii

Example Question #3625 : Algebra Ii

Example Question #3626 : Algebra Ii

Example Question #3627 : Algebra Ii

Example Question #161 : Simplifying Exponents

Example Question #162 : Simplifying Exponents

Example Question #163 : Simplifying Exponents

Example Question #164 : Simplifying Exponents

Example Question #165 : Simplifying Exponents

Example Question #163 : Multiplying And Dividing Exponents

All Algebra II Resources

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