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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #551 : Exponents

Evaluate:

$(5^{6})^7$ $\displaystyle (5^{6})^7$

Possible Answers:

25^5 $\displaystyle 25^5$

$5^{28}$ $\displaystyle 5^{28}$

$5^{42}$ $\displaystyle 5^{42}$

$5^{20}$ $\displaystyle 5^{20}$

$5^{13}$ $\displaystyle 5^{13}$

Correct answer:

$5^{42}$ $\displaystyle 5^{42}$

Explanation:

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

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

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Example Question #1021 : Mathematical Relationships And Basic Graphs

Evaluate:

(9^9)^9 $\displaystyle (9^9)^9$

Possible Answers:

$9^{99}$ $\displaystyle 9^{99}$

$81^{9}$ $\displaystyle 81^{9}$

$9^{81}$ $\displaystyle 9^{81}$

$81^{18}$ $\displaystyle 81^{18}$

$9^{18}$ $\displaystyle 9^{18}$

Correct answer:

$9^{81}$ $\displaystyle 9^{81}$

Explanation:

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

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

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Example Question #1022 : Mathematical Relationships And Basic Graphs

Evaluate:

$(3^{15})^7$ $\displaystyle (3^{15})^7$

Possible Answers:

$9^{12}$ $\displaystyle 9^{12}$

$9^{15}$ $\displaystyle 9^{15}$

$3^{105}$ $\displaystyle 3^{105}$

$3^{22}$ $\displaystyle 3^{22}$

$3^{42}$ $\displaystyle 3^{42}$

Correct answer:

$3^{105}$ $\displaystyle 3^{105}$

Explanation:

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

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

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Example Question #1023 : Mathematical Relationships And Basic Graphs

Evaluate:

$\displaystyle (18^5)^5$

Possible Answers:

$18^{55}$ $\displaystyle 18^{55}$

$18^{25}$ $\displaystyle 18^{25}$

$90^{25}$ $\displaystyle 90^{25}$

$90^{5}$ $\displaystyle 90^{5}$

$18^{10}$ $\displaystyle 18^{10}$

Correct answer:

$18^{25}$ $\displaystyle 18^{25}$

Explanation:

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

Therefore:

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

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Example Question #1024 : Mathematical Relationships And Basic Graphs

Evaluate:

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

Possible Answers:

$\displaystyle 8$

$\frac{1}{8}$ $\displaystyle \frac{1}{8}$

$\frac{1}{16}$ $\displaystyle \frac{1}{16}$

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

$\displaystyle 16$

Correct answer:

$\frac{1}{8}$ $\displaystyle \frac{1}{8}$

Explanation:

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

Therefore:

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

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Example Question #225 : Simplifying Exponents

Simplify:

$\displaystyle (x+y)^2+(xy)^2$

Possible Answers:

$\displaystyle x^2+4xy+y^2$

$\displaystyle x^2+2xy+y^2+x^2y^2$

$\displaystyle 2x^2+2y^2$

$\displaystyle x^2+y^2+x^2y^2$

Correct answer:

$\displaystyle x^2+2xy+y^2+x^2y^2$

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:

$\displaystyle (x+y)(x+y)=x^2+2xy+y^2$

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

$\displaystyle (xy)^2=x^2y^2$

Adding the two together, we get

$\displaystyle x^2+2xy+y^2+x^2y^2$

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Example Question #1025 : Mathematical Relationships And Basic Graphs

Simplify: (2^5)^9 $\displaystyle (2^5)^9$

Possible Answers:

$2^{45}$ $\displaystyle 2^{45}$

$2^{24}$ $\displaystyle 2^{24}$

$2^{88}$ $\displaystyle 2^{88}$

$2^{14}$ $\displaystyle 2^{14}$

$2^{16}$ $\displaystyle 2^{16}$

Correct answer:

$2^{45}$ $\displaystyle 2^{45}$

Explanation:

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

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

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Example Question #1026 : Mathematical Relationships And Basic Graphs

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

Possible Answers:

$17^{-12}$ $\displaystyle 17^{-12}$

17^4 $\displaystyle 17^4$

$17^{-32}$ $\displaystyle 17^{-32}$

$17^{8}$ $\displaystyle 17^{8}$

$17^{-4}$ $\displaystyle 17^{-4}$

Correct answer:

$17^{-32}$ $\displaystyle 17^{-32}$

Explanation:

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

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

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Example Question #1027 : Mathematical Relationships And Basic Graphs

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

Possible Answers:

$3^{-36}$ $\displaystyle 3^{-36}$

$3^{-18}$ $\displaystyle 3^{-18}$

$\displaystyle 3$

$3^{81}$ $\displaystyle 3^{81}$

$3^{-9}$ $\displaystyle 3^{-9}$

Correct answer:

$3^{81}$ $\displaystyle 3^{81}$

Explanation:

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

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

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Example Question #1028 : Mathematical Relationships And Basic Graphs

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

Possible Answers:

$2^{17}$ $\displaystyle 2^{17}$

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

$2^{72}$ $\displaystyle 2^{72}$

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

4^6 $\displaystyle 4^6$

Correct answer:

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

Explanation:

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

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

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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #551 : Exponents

Example Question #1021 : Mathematical Relationships And Basic Graphs

Example Question #1022 : Mathematical Relationships And Basic Graphs

Example Question #1023 : Mathematical Relationships And Basic Graphs

Example Question #1024 : Mathematical Relationships And Basic Graphs

Example Question #225 : Simplifying Exponents

Example Question #1025 : Mathematical Relationships And Basic Graphs

Example Question #1026 : Mathematical Relationships And Basic Graphs

Example Question #1027 : Mathematical Relationships And Basic Graphs

Example Question #1028 : Mathematical Relationships And Basic Graphs

All Algebra II Resources

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