Select the equivalent expression. (5^(4)*b^(-10))^(-6)=? Choose 1 answer: (A) (b^(60))/(5^(24)) (B) 5^(4)*b^(60) (c) 5^(24)*b^(60)

Apply Power Rule: Apply the power of a power rule. The power of a power rule states that (x^m)^n = x^(m*n). We will apply this rule to both 5^4 and b^(-10) with the exponent of -6. (5^(4)*b^(-10))^(-6) = 5^(4*(-6)) * b^(-10*(-6))Multiply Exponents: Perform the multiplication of the exponents. Now we multiply the exponents for both 5 and b. 5^(4*(-6)) = 5^(-24) b^(-10*(-6)) = b^(60)Combine Results: Combine the results. We combine the results from Step 2 to get the simplified expression. 5^(-24) * b^(60)Rewrite with Positive Exponents: Rewrite the expression with positive exponents. Since 5^(-24) is in the numerator, we can rewrite it with a positive exponent by placing it in the denominator. (5^(-24) * b^(60)) = (b^(60)) / (5^(24))Match Given Options: Match the result with the given options. The expression we have obtained is (b^(60)) / (5^(24)), which matches option (A).

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Math Problems

Grade 8

Evaluate expressions using properties of exponents

Full solution

Q. Select the equivalent expression.

\newline

(5^{4}\cdot b^{-10})^{-6}=

\newline

Choose

1

answer:

\newline

(A)

\frac{b^{60}}{5^{24}}

\newline

(B)

5^{4}\cdot b^{60}

\newline

(C)

5^{24}\cdot b^{60}

Apply Power Rule: Apply the power of a power rule. $\newline$ The power of a power rule states that $(x^m)^n = x^{(m*n)}$ . We will apply this rule to both $5^4$ and $b^{(-10)}$ with the exponent of $-6$ . $\newline$ $(5^{(4)}*b^{(-10)})^{(-6)} = 5^{(4*(-6))} * b^{(-10*(-6))}$
Multiply Exponents: Perform the multiplication of the exponents. $\newline$ Now we multiply the exponents for both $5$ and $b$ . $\newline$ $5^{4*(-6)} = 5^{-24}$ $\newline$ $b^{(-10)*(-6)} = b^{60}$
Combine Results: Combine the results. $\newline$ We combine the results from Step $2$ to get the simplified expression. $\newline$ $5^{-24} \times b^{60}$
Rewrite with Positive Exponents: Rewrite the expression with positive exponents. $\newline$ Since $5^{-24}$ is in the numerator, we can rewrite it with a positive exponent by placing it in the denominator. $\newline$ $(5^{-24} \cdot b^{60}) = \frac{b^{60}}{5^{24}}$
Match Given Options: Match the result with the given options. $\newline$ The expression we have obtained is $\frac{b^{60}}{5^{24}}$ , which matches option (A).