Which expressions are equivalent to 7^(-2)*7^(6) ? Choose 2 answers: A (7^(2))/(7^(-2)) B (7^(6))/(7^(-2)) c 7^(-12) D (7^(2))^(2)

Simplify using properties of exponents: Simplify the expression using the properties of exponents. When multiplying powers with the same base, you add the exponents. 7^(-2)*7^(6) = 7^(-2+6) = 7^(4)Compare to answer choices: Compare the simplified expression to the answer choices. We have simplified the expression to 7^(4). Now we need to determine which of the given choices are equivalent to this expression. A) (7^(2))/(7^(-2)) = 7^(2 - (-2)) = 7^(2 + 2) = 7^(4) B) (7^(6))/(7^(-2)) = 7^(6 - (-2)) = 7^(6 + 2) = 7^(8) C) 7^(-12) is not equivalent to 7^(4) because the exponents are different. D) (7^(2))^(2) = 7^(2*2) = 7^(4) Choices A and D are equivalent to 7^(4).

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Math Problems

Grade 8

Evaluate expressions using properties of exponents

Full solution

Q. Which expressions are equivalent to

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7^{-2} \cdot 7^{6}

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Choose

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2

answers:

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\frac{7^{2}}{7^{-2}}

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\frac{7^{6}}{7^{-2}}

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7^{-12}

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(7^{2})^{2}

Simplify using properties of exponents: Simplify the expression using the properties of exponents. $\newline$ When multiplying powers with the same base, you add the exponents. $\newline$ $7^{-2}\times7^{6} = 7^{-2+6} = 7^{4}$
Compare to answer choices: Compare the simplified expression to the answer choices. $\newline$ We have simplified the expression to $7^{4}$ . Now we need to determine which of the given choices are equivalent to this expression. $\newline$ A) $(7^{2})/(7^{-2}) = 7^{2 - (-2)} = 7^{2 + 2} = 7^{4}$ $\newline$ B) $(7^{6})/(7^{-2}) = 7^{6 - (-2)} = 7^{6 + 2} = 7^{8}$ $\newline$ C) $7^{-12}$ is not equivalent to $7^{4}$ because the exponents are different. $\newline$ D) $(7^{2})^{2} = 7^{2*2} = 7^{4}$ $\newline$ Choices A and D are equivalent to $7^{4}$ .