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Algebra II : Distributing Exponents (Power Rule)

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Example Question #31 : Distributing Exponents (Power Rule)

Simplify:

$(24^{12})^{\frac{1}{18}}$

Possible Answers:

$4\sqrt[3]{9}$

$9\sqrt[3]{4}$

$24\sqrt[3]{2}$

Correct answer:

$4\sqrt[3]{9}$

Explanation:

When exponents are being raised by another exponent, we just multiply the powers.

$(24^{12})^{\frac{1}{18}}=24^{12*\frac{1}{18}}=24^{\frac{2}{3}}$

When we have fractional exponents, we convert like this:

$x^{\frac{a}b{}}=\sqrt[b]{x^a}$ . is the index of the radical which is the denominator of the fractional exponent, is the power that will raise the base which is the numerator of the fractional exponent and is the base.

$24^{\frac{2}{3}}=\sqrt[3]{24^2}=\sqrt[3]{576}$ The perfect cube we can get is .

$\sqrt[3]{576}=\sqrt[3]{64*9}=4\sqrt[3]{9}$

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Example Question #211 : Simplifying Exponents

Evaluate:

(2^9)^4

Possible Answers:

$2^{13}$

8^9

$2^{36}$

4^8

$4^{10}$

Correct answer:

$2^{36}$

Explanation:

When dealing exponents being raised by a power, we multiply the exponents and keep the base.

$(2^9)^4=2^{9*4}=2^{36}$

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Example Question #212 : Simplifying Exponents

Evaluate:

$(5^{6})^7$

Possible Answers:

$5^{13}$

$5^{20}$

$5^{28}$

$5^{42}$

25^5

Correct answer:

$5^{42}$

Explanation:

When dealing exponents being raised by a power, we multiply the exponents and keep the base.

$(5^{6})^7=5^{6*7}=5^{42}$

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Example Question #221 : Simplifying Exponents

Evaluate:

(9^9)^9

Possible Answers:

$9^{18}$

$9^{81}$

$9^{99}$

$81^{18}$

$81^{9}$

Correct answer:

$9^{81}$

Explanation:

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

$(9^9)^9=9^{9*9}=9^{81}$

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Example Question #31 : Distributing Exponents (Power Rule)

Evaluate:

$(3^{15})^7$

Possible Answers:

$9^{15}$

$3^{42}$

$3^{105}$

$3^{22}$

$9^{12}$

Correct answer:

$3^{105}$

Explanation:

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

$(3^{15})^7=3^{15*7}=3^{105}$

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Example Question #222 : Simplifying Exponents

Evaluate:

(18^5)^5

Possible Answers:

$18^{55}$

$18^{25}$

$90^{5}$

$90^{25}$

$18^{10}$

Correct answer:

$18^{25}$

Explanation:

When an exponent is raised by another power, we will multiply the exponents and keep the base the same.

Therefore:

$(18^5)^5=18^{5*5}=18^{25}$

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Example Question #33 : Distributing Exponents (Power Rule)

Evaluate:

$\left(\left(\frac{1}{2}\right)^6\right)^{\frac{1}{2}}$

Possible Answers:

$\frac{1}{4}$

$\frac{1}{16}$

$\frac{1}{8}$

Correct answer:

$\frac{1}{8}$

Explanation:

When an exponent is raised by another power, we will multiply the exponents and keep the base the same.

Therefore:

$\left(\left(\frac{1}{2}\right)^6\right)^{\frac{1}{2}}=\left(\frac{1}{2}\right)^{6*\frac{1}{2}}=\frac{1}{2^{3}}=\frac{1}{8}$

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Example Question #38 : Distributing Exponents (Power Rule)

Simplify:

(x+y)^2+(xy)^2

Possible Answers:

x^2+4xy+y^2

x^2+2xy+y^2+x^2y^2

2x^2+2y^2

x^2+y^2+x^2y^2

Correct answer:

x^2+2xy+y^2+x^2y^2

Explanation:

To start, we must examine the first term. Note that we are squaring a sum, so we cannot simply distribute the power of 2 to each term. We must take the sum times the sum:

(x+y)(x+y)=x^2+2xy+y^2

The second term, however, is a product, in which case we can distribute the power:

(xy)^2=x^2y^2

Adding the two together, we get

x^2+2xy+y^2+x^2y^2

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Example Question #32 : Distributing Exponents (Power Rule)

Simplify: (2^5)^9

Possible Answers:

$2^{16}$

$2^{88}$

$2^{14}$

$2^{45}$

$2^{24}$

Correct answer:

$2^{45}$

Explanation:

When an exponent is raised by another exponent, we just multiply the exponents and keep the base the same.

$(2^5)^9=2^{5*9}=2^{45}$

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Example Question #223 : Simplifying Exponents

Simplify: $(17^8)^{-4}$

Possible Answers:

$17^{-4}$

$17^{-12}$

$17^{-32}$

$17^{8}$

17^4

Correct answer:

$17^{-32}$

Explanation:

When an exponent is raised by another exponent, we just multiply the exponents and keep the base the same.

$(17^8)^{-4}=17^{8*-4}=17^{-32}$

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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 #31 : Distributing Exponents (Power Rule)

Example Question #211 : Simplifying Exponents

Example Question #212 : Simplifying Exponents

Example Question #221 : Simplifying Exponents

Example Question #31 : Distributing Exponents (Power Rule)

Example Question #222 : Simplifying Exponents

Example Question #33 : Distributing Exponents (Power Rule)

Example Question #38 : Distributing Exponents (Power Rule)

Example Question #32 : Distributing Exponents (Power Rule)

Example Question #223 : Simplifying Exponents

All Algebra II Resources

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