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 (a^m)^n = a^(m*n). We will apply this rule to both 5^(4) and b^(-10) separately. (5^(4)*b^(-10))^(-6) = (5^(4))^(-6) * (b^(-10))^(-6)Multiply Exponents: Multiply the exponents. Now we multiply the exponents for each base. (5^(4))^(-6) = 5^(4*(-6)) = 5^(-24) (b^(-10))^(-6) = b^(-10*(-6)) = b^(60)Combine Results: Combine the results. We now have two separate terms, 5^(-24) and b^(60). We combine them to form the final expression. (5^(4)*b^(-10))^(-6) = 5^(-24) * b^(60)Simplify with Negative Exponent: Simplify the expression with negative exponent. The term 5^(-24) can be rewritten as 1/(5^(24)) because a negative exponent indicates the reciprocal of the base raised to the positive exponent. 5^(-24) * b^(60) = (1/(5^(24))) * b^(60)Rearrange Expression: Rearrange the expression. We can rearrange the expression to match the answer choices. (1/(5^(24))) * b^(60) = b^(60) / (5^(24))Match with Answer Choices: Match the expression with the answer choices. The expression b^(60) / (5^(24)) matches answer choice (A).

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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)

Select the equivalent expression. $\newline$ $\left(5^{4} \cdot b^{-10}\right)^{-6}=?$ $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{b^{60}}{5^{24}}$ $\newline$ (B) $5^{4} \cdot b^{60}$ $\newline$ (C) $5^{24} \cdot b^{60}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\left(5^{4} \cdot b^{-10}\right)^{-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 $(a^m)^n = a^{m*n}$ . We will apply this rule to both $5^{4}$ and $b^{-10}$ separately. $\newline$ $(5^{4}*b^{-10})^{-6} = (5^{4})^{-6} * (b^{-10})^{-6}$
Multiply Exponents: Multiply the exponents. $\newline$ Now we multiply the exponents for each base. $\newline$ $(5^{4})^{(-6)} = 5^{4*(-6)} = 5^{-24}$ $\newline$ $(b^{(-10)})^{(-6)} = b^{-10*(-6)} = b^{60}$
Combine Results: Combine the results. $\newline$ We now have two separate terms, $5^{-24}$ and $b^{60}$ . We combine them to form the final expression. $\newline$ $(5^{4}*b^{-10})^{-6} = 5^{-24} * b^{60}$
Simplify with Negative Exponent: Simplify the expression with negative exponent. $\newline$ The term $5^{-24}$ can be rewritten as $\frac{1}{5^{24}}$ because a negative exponent indicates the reciprocal of the base raised to the positive exponent. $\newline$ $5^{-24} \times b^{60} = \left(\frac{1}{5^{24}}\right) \times b^{60}$
Rearrange Expression: Rearrange the expression. $\newline$ We can rearrange the expression to match the answer choices. $\newline$ $\frac{1}{5^{24}}$ * $b^{60}$ = $\frac{b^{60}}{5^{24}}$
Match with Answer Choices: Match the expression with the answer choices. $\newline$ The expression $b^{60} / (5^{24})$ matches answer choice $(A)$ .