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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 #151 : Simplifying Exponents

Evaluate: x^5*2x^2

Possible Answers:

$2x^{10}$

$4x^{10}$

4x^7

4x^8

2x^7

Correct answer:

2x^7

Explanation:

When multiplying exponents, we just add the exponents and keep the base the same.

$x^5*2x^2=2x^{5+2}=2x^7$

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Example Question #152 : Simplifying Exponents

Evaluate: $3x^7*4x^{-2}$

Possible Answers:

12x^9

$3^74^{-2}x^9$

$12x^{-14}$

12x^5

$3^74^{-2}x^5$

Correct answer:

12x^5

Explanation:

When multiplying exponents, we just add the exponents and keep the base the same.

$3x^7*4x^{-2}=12x^{7+(-2)}=12x^5$

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Example Question #153 : Simplifying Exponents

Simplify: $\frac{8^{2x}}{8^{2x-1}}$

Possible Answers:

$8^{2x}$

$\frac{1}{8^{2x}}$

Correct answer:

Explanation:

When dividing exponents, we just subtract the exponents and keep the base the same.

$\frac{8^{2x}}{8^{2x-1}}=8^{2x-(2x-1)}=8^{2x-2x+1}=8^{1}=8$

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Example Question #154 : Simplifying Exponents

Simplify: $\frac{x^5y^7}{x^{5+b}y^{7-c}}$

Possible Answers:

x^by^c

$\frac{y^c}{x^b}$

-x^by^c

$\frac{x^b}{y^c}$

$xy^{b-c}$

Correct answer:

$\frac{y^c}{x^b}$

Explanation:

When dividing exponents, we just subtract the exponents and keep the base the same.

$\frac{x^5y^7}{x^{5+b}y^{7-c}}=x^{5-(5+b)y^{7-(7-c)}}=x^{-b}y^c=\frac{y^c}{x^b}$

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Example Question #155 : Multiplying And Dividing Exponents

Solve the exponents: $4(2^{30})(8^{50})$

Possible Answers:

$4^{182}$

$64^{80}$

$32^{80}$

$8^{182}$

$2^{182}$

Correct answer:

$2^{182}$

Explanation:

To simplify, we will need to convert all bases to a common base to apply exponent properties.

2=2^1, 4=2^2, 8=2^3

We can rewrite each term using the powers of two.

$4(2^{30})(8^{50}) = (2^2)(2^{30})(2^{3(50)})= (2^2)(2^{30})(2^{150})$

Simplify the exponents. Since powers of same bases are multiplied, the powers can be added.

$2^{2+30+150} = 2^{182}$

The answer is: $2^{182}$

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Example Question #156 : Multiplying And Dividing Exponents

Divide: $\frac{6^{-2}}{3^{-3}}$

Possible Answers:

$\frac{4}{3}$

$\frac{1}{32}$

$\frac{3}{4}$

Correct answer:

$\frac{3}{4}$

Explanation:

Simplify the negative exponents by rewriting the terms as fractions.

$\frac{6^{-2}}{3^{-3}} = \frac{\frac{1}{6^2}}{\frac{1}{3^3}}= \frac{\frac{1}{36}}{\frac{1}{27}}$

Divide the complex fractions.

$\frac{1}{36} \div \frac{1}{27} = \frac{1}{36} \times 27 =\frac{27}{36}$

Reduce this fraction.

The answer is: $\frac{3}{4}$

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Example Question #157 : Multiplying And Dividing Exponents

Divide the exponents: $\frac{8^6}{4^8}$

Possible Answers:

$\frac{1}{4}$

$\frac{1}{2}$

Correct answer:

Explanation:

Change the base of the numerator and denominator.

They both can be rewritten as a base of two.

$\frac{8^6}{4^8} = \frac{2^{3(6)}}{2^{2(8)}} = \frac{2^{18}}{2^{16}}$

Since the bases are similar, we can subtract the exponents.

$2^{18-16} = 2^2 =4$

The answer is:

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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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Algebra II : Multiplying and Dividing Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #151 : Simplifying Exponents

Example Question #152 : Simplifying Exponents

Example Question #153 : Simplifying Exponents

Example Question #154 : Simplifying Exponents

Example Question #155 : Multiplying And Dividing Exponents

Example Question #156 : Multiplying And Dividing Exponents

Example Question #157 : Multiplying And Dividing Exponents

Example Question #155 : Simplifying Exponents

Example Question #156 : Simplifying Exponents

Example Question #3623 : Algebra Ii

All Algebra II Resources

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