Select the equivalent expression. ((4^(3))/(5^(-2)))^(5)=? Choose 1 answer: (A) (4^(8))/(5^(3)) (B) (4^(15))/(5^(10)) (c) 4^(15)*5^(10)

Apply Power Rule: Apply the power of a power rule. The power of a power rule states that (a^(m))^n = a^(m*n). We will apply this rule to both the numerator and the denominator separately. ((4^(3))/(5^(-2)))^(5) = (4^(3*5))/(5^(-2*5))Multiply Exponents: Perform the multiplication for the exponents. Now we multiply the exponents by 5. 4^(3*5) = 4^(15) 5^(-2*5) = 5^(-10)Rewrite Expression: Rewrite the expression with the new exponents. We now have the expression (4^(15))/(5^(-10)).Simplify Exponents: Simplify the expression by converting the negative exponent to a positive exponent. A negative exponent means that the base is on the wrong side of the fraction line, so we flip it to the other side to make the exponent positive. (4^(15))/(5^(-10)) = 4^(15) * 5^(10)Choose Correct Answer: Choose the correct answer. The expression 4^(15) * 5^(10) matches answer choice (C).

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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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\left(\frac{4^{3}}{5^{-2}}\right)^{5}=\,?

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Choose

1

answer:

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(A)

\frac{4^{8}}{5^{3}}

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(B)

\frac{4^{15}}{5^{10}}

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(C)

4^{15}\cdot 5^{10}

Apply Power Rule: Apply the power of a power rule. $\newline$ The power of a power rule states that $(a^{m})^{n} = a^{m*n}$ . We will apply this rule to both the numerator and the denominator separately. $\newline$ $\left(\frac{4^{3}}{5^{-2}}\right)^{5} = \frac{4^{3*5}}{5^{-2*5}}$
Multiply Exponents: Perform the multiplication for the exponents. $\newline$ Now we multiply the exponents by $5$ . $\newline$ $4^{(3\times5)} = 4^{15}$ $\newline$ $5^{(-2\times5)} = 5^{-10}$
Rewrite Expression: Rewrite the expression with the new exponents. $\newline$ We now have the expression $(4^{15})/(5^{-10})$ .
Simplify Exponents: Simplify the expression by converting the negative exponent to a positive exponent. $\newline$ A negative exponent means that the base is on the wrong side of the fraction line, so we flip it to the other side to make the exponent positive. $\newline$ $\frac{4^{15}}{5^{-10}} = 4^{15} \times 5^{10}$
Choose Correct Answer: Choose the correct answer. $\newline$ The expression $4^{15} \times 5^{10}$ matches answer choice (C).