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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 #381 : Exponents

Simplify.

$x^{15}*x^{17}$

Possible Answers:

$x^{32}$

$x^{-2}$

$x^{255}$

$x^{22}$

$x^{285}$

Correct answer:

$x^{32}$

Explanation:

When multiplying exponents with the same base, you just have to add the exponents.

$x^{15}*x^{17}=x^{15+17}=x^{32}$

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Example Question #51 : Simplifying Exponents

Simplify.

$3^{-14}*3^{23}*3^{-15}$

Possible Answers:

$3^{-6}$

$27^{-6}$

3^6

27^6

$9^{-6}$

Correct answer:

$3^{-6}$

Explanation:

When multiplying exponents with the same base, you just have to add the exponents.

$3^{-14}*3^{23}*3^{-15}=3^{-14+23-15}=3^{-6}$

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Example Question #52 : Simplifying Exponents

Simplify.

$\frac{a^{45}}{a^{30}}$

Possible Answers:

$a^{2.5}$

$a^{15}$

$a^{75}$

a^5

$a^{1.5}$

Correct answer:

$a^{15}$

Explanation:

When dividing exponents with the same base, we just subtract the exponents.

$\frac{a^{45}}{a^{30}}=a^{45-30}=a^{15}$

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Example Question #53 : Simplifying Exponents

Simplify.

$\frac{a^7}{a^{18}}$

Possible Answers:

$a^{-11}$

$a^{11}$

$a^{-25}$

$a^{25}$

$a^{\frac{7}{18}}$

Correct answer:

$a^{-11}$

Explanation:

When dividing exponents with the same base, we just subtract the exponents.

$\frac{a^{7}}{a^{18}}=a^{7-18}=a^{-11}$

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Example Question #54 : Simplifying Exponents

Simplify.

$2^{12}*2^{16}*2^{14}$

Possible Answers:

$8^{44}$

$4^{24}$

$2^{42}$

$2^{36}$

$8^{28}$

Correct answer:

$2^{42}$

Explanation:

When multiplying exponents with the same base, you just have to add the exponents.

$2^{12}*2^{16}*2^{14}=2^{12+16+14}=2^{42}$

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Example Question #55 : Simplifying Exponents

Simplify.

$x^{-24}*x^{21}*y^6$

Possible Answers:

$x^{-3}*y^6$

x^3*y^6

$x^{-504}*y^6$

$x^{-504}$

x^3

Correct answer:

$x^{-3}*y^6$

Explanation:

When multiplying exponents with the same base, you just have to add the exponents.

$x^{-24}*x^{21}*y^6=x^{-24+21}*y^6=x^{-3}*y^6$

We just keep as it is.

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Example Question #56 : Multiplying And Dividing Exponents

Simplify.

$\frac{a^9b^{11}}{a^{10}b^7}$

Possible Answers:

$\frac{b^4}{a}$

$a^{19}b^{18}$

$a^{90}b^{77}$

ab^3

$\frac{a}{b^4}$

Correct answer:

$\frac{b^4}{a}$

Explanation:

When dividing exponents with the same base, we just subtract the exponents.

$\frac{a^{9}b^{11}}{a^{10}b^7}=a^{9-10}*b^{11-7}=a^{-1}*b^4$ $a^{-1}$ is the same as $\frac{1}{a}$ .

Final answer is $\frac{b^4}{a}$ .

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Example Question #57 : Multiplying And Dividing Exponents

Simplify.

$\frac{a^{23}b^{12}}{a^{25}b^{15}}$

Possible Answers:

$a^{48}b^{27}$

$\frac{1}{a^2b^3}$

-(ab)^6

ab^6

a^2b^3

Correct answer:

$\frac{1}{a^2b^3}$

Explanation:

When dividing exponents with the same base, we just subtract the exponents.

$\frac{a^{23}b^{12}}{a^{25}b^{15}}=a^{23-25}*b^{12-15}=a^{-2}*b^{-3}$ $a^{-2}$ is the same as $\frac{1}{a^2}$ and $b^{-3}$ is the same as $\frac{1}{b^3}$ .

Final answer is $\frac{1}{a^2b^3}$ .

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Example Question #56 : Simplifying Exponents

Simplify the expression:

$\frac{4^{36}}{4^{6}}$

Possible Answers:

4^6

$4^{12}$

$4^{30}$

$4^{42}$

Correct answer:

$4^{30}$

Explanation:

When dividing exponents with the same coefficient, you subtract the exponents. 36-6=30

Therefore the answer is $4^{30}$ .

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Example Question #59 : Multiplying And Dividing Exponents

Simplify $\frac{a^{4}b^{8}c^{9}d^{7}}{a^{2}bc^{6}}$

Possible Answers:

$a^{2}b^{7}c^{3}d^{7}$

$d^{7}$

$\frac{a^{6}b^{9}c^{3}}{d^{7}}$

$a^{6}b^{9}c^{15}d^{7}$

$\frac{a^{4}b^{6}}{d^{7}}$

Correct answer:

$a^{2}b^{7}c^{3}d^{7}$

Explanation:

Same variables with exponents in a numerator and denominator of a fraction cancel each other out. It can be thought of as you take the exponent of the variable in the numerator and subtract it by the exponent of the same variable in the denominator.

$\frac{a^{4}b^{8}c^{9}d^{7}}{a^{2}bc^{6}}$

Can be written as

$a^{4-2}b^{8-1}c^{9-6}d^{7}$

$a^{2}b^{7}c^{3}d^{7}$

This is as far as you can simplify.

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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 #381 : Exponents

Example Question #51 : Simplifying Exponents

Example Question #52 : Simplifying Exponents

Example Question #53 : Simplifying Exponents

Example Question #54 : Simplifying Exponents

Example Question #55 : Simplifying Exponents

Example Question #56 : Multiplying And Dividing Exponents

Example Question #57 : Multiplying And Dividing Exponents

Example Question #56 : Simplifying Exponents

Example Question #59 : Multiplying And Dividing Exponents

All Algebra II Resources

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