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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #155 : Simplifying Exponents

Divide: $\frac{a^3c}{a^6b^{-3}c^{-9}}$

Possible Answers:

$\frac{1}{a^3b^3c^{10}}$

$\frac{c^{10}}{a^3b^3}$

$\frac{b^3c^{10}}{a^3}$

$\frac{b^3}{a^3c^{10}}$

$\frac{b^3}{a^3c^8}$

Correct answer:

$\frac{b^3c^{10}}{a^3}$

Explanation:

For the common bases that are divided, the exponents can be subtract from numerator to denominator.

Evaluate the terms.

$\frac{a^3}{a^6} = a^{3-6} = a^{-3} = \frac{1}{a^3}$

Since there is no term on the numerator, we can assume $b^{0}=1$ .

$\frac{b^{0}}{b^{-3}} = \frac{1}{b^{-3}}= \frac{1}{\frac{1}{b^3}} = b^3$

$\frac{c^1}{c^{-9}} = c^{1-(-9)} = c^{10}$

Multiply the three terms together.

$\frac{1}{a^3}\cdot b^3 \cdot c^{10} = \frac{b^3c^{10}}{a^3}$

The answer is: $\frac{b^3c^{10}}{a^3}$

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Example Question #156 : Simplifying Exponents

Solve: $\frac{4^{500}\times 2^{250}}{8^{125}}$

Possible Answers:

$2^{875}$

$4^{625}$

$2^{630}$

$2^{625}$

Correct answer:

$2^{875}$

Explanation:

To be able to add or subtract exponents, we should change the bases so that every base is common.

Four is two squared, and eight is two cubed. We can rewrite the numbers using base two.

$\frac{4^{500}\times 2^{250}}{8^{125}}=\frac{2^{2(500)}\times 2^{250}}{2^{3(125)}}= \frac{2^{1000}\times 2^{250}}{2^{375}}$

When exponents of the same bases are multiplied, the powers can be added. When exponents of the same base are divided, their powers can be subtracted.

$2^{1000+250-375} = 2^{875}$

The answer is: $2^{875}$

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Example Question #3623 : Algebra Ii

Multiply: 2^0(2^2)^3

Possible Answers:

128

$\textup{The answer is not given.}$

Correct answer:

$\textup{The answer is not given.}$

Explanation:

The quantity of two squared raised to the third power can be simplified by multiplying the two powers together.

(2^2)^3 =2^6

The expression becomes: 2^0(2^2)^3 = 2^0(2^6)

When common bases of powers are multiplied with each other, we can add the powers together.

$2^{0+6}=2^6 = 64$

The answer is: $\textup{The answer is not given.}$

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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 #491 : Exponents

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

Possible Answers:

x^14

x^1

x^6

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 #492 : Exponents

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

Possible Answers:

$x^{-2}$

x^3

x^3/x^2

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 #493 : Exponents

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

Possible Answers:

$x^{28}$

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

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

$x^{18}$

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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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #155 : Simplifying Exponents

Example Question #156 : Simplifying Exponents

Example Question #3623 : Algebra Ii

Example Question #3624 : Algebra Ii

Example Question #3625 : Algebra Ii

Example Question #3626 : Algebra Ii

Example Question #3627 : Algebra Ii

Example Question #491 : Exponents

Example Question #492 : Exponents

Example Question #493 : Exponents

All Algebra II Resources

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