Select the equivalent expression. ((x^(4))/(7^(-8)))^(-7)=? Choose 1 answer: (A) x^(-28)*7^(-56) (B) (x^(28))/(7^(56)) (c) (x^(28))/(7^(-56))

Apply Quotient Rule: Apply the power of a quotient rule. The power of a quotient rule states that (a/b)^n = a^n / b^n. We will apply this rule to the given expression ((x^(4))/(7^(-8)))^(-7). ((x^(4))/(7^(-8)))^(-7) = (x^(4))^(-7) / (7^(-8))^(-7)Simplify Exponents: Simplify the exponents. When raising a power to a power, you multiply the exponents. So, (x^(4))^(-7) becomes x^(4 * -7) and (7^(-8))^(-7) becomes 7^(-8 * -7). (x^(4))^(-7) / (7^(-8))^(-7) = x^(-28) / 7^(56)Write Final Expression: Write the final expression. The simplified expression is x^(-28) / 7^(56), which corresponds to one of the answer choices.

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Math Problems

Grade 8

Evaluate expressions using properties of exponents

Full solution

Q. Select the equivalent expression.

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((x^{4})/(7^{-8}))^{-7}=

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Choose

1

answer:

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(A)

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x^{-28}\cdot7^{56}

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(B)

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(x^{28})/(7^{56})

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(C)

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(x^{28})/(7^{-56})

Apply Quotient Rule: Apply the power of a quotient rule. $\newline$ The power of a quotient rule states that $(\frac{a}{b})^n = \frac{a^n}{b^n}$ . We will apply this rule to the given expression $\left(\frac{x^{4}}{7^{-8}}\right)^{-7}$ . $\newline$ $\left(\frac{x^{4}}{7^{-8}}\right)^{-7} = \frac{(x^{4})^{-7}}{(7^{-8})^{-7}}$
Simplify Exponents: Simplify the exponents. $\newline$ When raising a power to a power, you multiply the exponents. So, $(x^{4})^{-7}$ becomes $x^{4 \cdot -7}$ and $(7^{-8})^{-7}$ becomes $7^{-8 \cdot -7}$ . $\newline$ $\frac{(x^{4})^{-7}}{(7^{-8})^{-7}} = \frac{x^{-28}}{7^{56}}$
Write Final Expression: Write the final expression. $\newline$ The simplified expression is $x^{-28} / 7^{56}$ , which corresponds to one of the answer choices.