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Algebra II : Distributing Exponents (Power Rule)

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Example Questions

Example Question #243 : Simplifying Exponents

Simplify: $(4^{10})^{-3}$

Possible Answers:

$4^{-30}$

$4^{-13}$

$16^{-3}$

4^7

$8^{30}$

Correct answer:

$4^{-30}$

Explanation:

When dealing with exponents being raised by another exponent, we just multiply the powers and keep the base the same.

$(4^{10})^{-3}=4^{10*-3}=4^{-30}$

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Example Question #62 : Distributing Exponents (Power Rule)

Simplify:

(a^3b^3)^2(a^2b^2)^3

Possible Answers:

$a^{10}b^{10}$

$a^{6}b^{6}$

$a^{12}b^{12}$

None of these

$a^{4}b^{4}$

Correct answer:

$a^{12}b^{12}$

Explanation:

Exponents outside of a parentheses are distributed through multiplication:

(a^3b^3)^2

becomes

a^6b^6

(a^2b^2)^3

becomes

a^6b^6

$a^6b^6*a^6b^6=a^{12}b^{12}$

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Example Question #244 : Simplifying Exponents

Simplify:

$(5^{-8})^{-12}$

Possible Answers:

$5^{96}$

$25^{-20}$

$5^{-96}$

25^8

$5^{-20}$

Correct answer:

$5^{96}$

Explanation:

When dealing with exponents being raised by another exponent, we just multiply the powers and keep the base the same.

$(5^{-8})^{-12}=5^{-8*-12}=5^{96}$

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Example Question #251 : Simplifying Exponents

Expand and simplify: [1+(2^2)^3]^2

Possible Answers:

531441

1089

4225

4096

4097

Correct answer:

4225

Explanation:

Evaluate the exponential term inside the bracket first. Use the product rule for exponents to simplify.

$(2^2)^3 = (2^2)(2^2)(2^2) = 2^{2\cdot 3} = 2^6 = 64$

The term inside the bracket becomes:

[1+64]^2

Simplify the term inside.

65^2 = 4225

The answer is: 4225

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Example Question #252 : Simplifying Exponents

Solve: $(4^{150})^{5}$

Possible Answers:

$1024^{155}$

$4^{180}$

$4^{750}$

$4^{155}$

$1024^{30}$

Correct answer:

$4^{750}$

Explanation:

When the quantity of the terms of a base raised to a power is also raised to a power, we can use the product rule for exponents to expand this expression.

$(X^Y)^Z = X^{YZ}$

Multiply the powers together.

$(4^{150})^{5} = 4^{150\cdot 5} = 4^{750}$

The answer is: $4^{750}$

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Example Question #251 : Simplifying Exponents

Simplify: (8x^3)^2

Possible Answers:

64x^6

8x^6

16x^5

16x^6

Correct answer:

64x^6

Explanation:

$When\ raising\ a\ power\ to\ a\ power\ multiply\ the\ exponents.$

(8x^3)^2=8^2x^(^3^*^2^)=64x^6

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Example Question #254 : Simplifying Exponents

Simplify the exponents: $(2^3)^{-2}+(4^0)^3$

Possible Answers:

$\frac{1}{2}$

$\frac{65}{64}$

$\frac{13}{12}$

128

Correct answer:

$\frac{65}{64}$

Explanation:

To simplify this expression, since the powers are outside of a quantity of a power, we can multiply the powers together according to the power rule.

$(x^a)^b = x^{ab}$

Simplify the expression.

$(2^3)^{-2}+(4^0)^3 = 2^{-6}+4^0$

Change the negative exponent into a fraction and simplify.

$2^{-6}+4^0 = \frac{1}{2^6}+1 = \frac{1}{64}+\frac{64}{64}$

The answer is: $\frac{65}{64}$

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Example Question #255 : Simplifying Exponents

Simplify: $(\frac{1}{3^3})^{-2}$

Possible Answers:

243

$\frac{1}{243}$

$\frac{1}{3}$

$\frac{1}{729}$

729

Correct answer:

729

Explanation:

The fraction inside the parentheses can be rewritten as a negative exponent.

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

Using the power property of exponents, multiply both exponents together.

$(3^{-3})^{-2} = 3^6$

Simplify this value.

$3^6 = 3\cdot3\cdot3\cdot3\cdot3\cdot3 = 729$

The answer is: 729

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Example Question #256 : Simplifying Exponents

Simplify: $(3^{11}\cdot 3^{10})^3$

Possible Answers:

$3^{24}$

$3^{330}$

$3^{63}$

$3^{113}$

$9^{330}$

Correct answer:

$3^{63}$

Explanation:

Determine the inner term by using the additive rule of exponents. When the bases of a certain power are similar, the powers can be added.

$(3^{11}\cdot 3^{10})^3 =(3^{11+10})^3 = (3^{21})^3$

Use the power rule to simplify this term.

$(3^{21})^3 = 3^{21\times 3} = 3^{63}$

The answer is: $3^{63}$

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Example Question #252 : Simplifying Exponents

Simplify: $(2x^{55})^{2}$

Possible Answers:

$2x^{110}$

$4x^{110}$

$2x^{107}$

$4x^{57}$

$2x^{57}$

Correct answer:

$4x^{110}$

Explanation:

According to the rule of exponents, we can distribute the power of two by multiplying the powers.

$(2x^{55})^{2} = (2x^{55})(2x^{55}) = (2^{1\times 2}x^{55 \times 2})$

Simplify the terms.

The answer is: $4x^{110}$

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Algebra II : Distributing Exponents (Power Rule)

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #243 : Simplifying Exponents

Example Question #62 : Distributing Exponents (Power Rule)

Example Question #244 : Simplifying Exponents

Example Question #251 : Simplifying Exponents

Example Question #252 : Simplifying Exponents

Example Question #251 : Simplifying Exponents

Example Question #254 : Simplifying Exponents

Example Question #255 : Simplifying Exponents

Example Question #256 : Simplifying Exponents

Example Question #252 : Simplifying Exponents

All Algebra II Resources

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