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Algebra II : Simplifying Exponents

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Example Questions

Example Question #32 : Distributing Exponents (Power Rule)

Evaluate:

(9^9)^9

Possible Answers:

$9^{18}$

$81^{18}$

$9^{81}$

$9^{99}$

$81^{9}$

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 #33 : Distributing Exponents (Power Rule)

Evaluate:

$(3^{15})^7$

Possible Answers:

$9^{12}$

$3^{42}$

$3^{22}$

$3^{105}$

$9^{15}$

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 #34 : Distributing Exponents (Power Rule)

Evaluate:

(18^5)^5

Possible Answers:

$18^{10}$

$18^{55}$

$90^{25}$

$18^{25}$

$90^{5}$

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 #35 : 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 #37 : Distributing Exponents (Power Rule)

Simplify:

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

Possible Answers:

x^2+4xy+y^2

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

2x^2+2y^2

x^2+2xy+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 #36 : Distributing Exponents (Power Rule)

Simplify: (2^5)^9

Possible Answers:

$2^{88}$

$2^{24}$

$2^{45}$

$2^{16}$

$2^{14}$

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 #37 : Distributing Exponents (Power Rule)

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

Possible Answers:

$17^{-4}$

17^4

$17^{-12}$

$17^{-32}$

$17^{8}$

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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Example Question #1021 : Mathematical Relationships And Basic Graphs

Simplify: $(3^{-9})^{-9}$

Possible Answers:

$3^{-18}$

$3^{-36}$

$3^{81}$

$3^{-9}$

Correct answer:

$3^{81}$

Explanation:

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

$(3^{-9})^{-9}=3^{-9*-9}=3^{81}$

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Example Question #1022 : Mathematical Relationships And Basic Graphs

Simplify: $(\frac{1}{2}^{9})^8$

Possible Answers:

$\frac{1}{2}^{72}$

4^6

$2^{17}$

$\frac{1}{2}^{17}$

$2^{72}$

Correct answer:

$\frac{1}{2}^{72}$

Explanation:

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

$(\frac{1}{2}^{9})^8=\frac{1}{2}^{9*8}=\frac{1}{2}^{72}$

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Example Question #221 : Simplifying Exponents

Simplify: $(3a^2b^{-3}c^4)^2$

Possible Answers:

$\frac{a^4c^8}{b^6}$

$\frac{9a^4c^8}{b^3}$

$\frac{3a^4c^8}{b^6}$

$\frac{9a^4c^8}{b^6}$

Correct answer:

$\frac{9a^4c^8}{b^6}$

Explanation:

To simplify this expression, square every term in the parentheses:

$3^2a^4b^{-6}c^8$ .

Then simplify and get rid of the negative exponent by putting the b term on the denominator:

$\frac{9a^4c^8}{b^6}$ .

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Algebra II : Simplifying Exponents

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #32 : Distributing Exponents (Power Rule)

Example Question #33 : Distributing Exponents (Power Rule)

Example Question #34 : Distributing Exponents (Power Rule)

Example Question #35 : Distributing Exponents (Power Rule)

Example Question #37 : Distributing Exponents (Power Rule)

Example Question #36 : Distributing Exponents (Power Rule)

Example Question #37 : Distributing Exponents (Power Rule)

Example Question #1021 : Mathematical Relationships And Basic Graphs

Example Question #1022 : Mathematical Relationships And Basic Graphs

Example Question #221 : Simplifying Exponents

All Algebra II Resources

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