Select the equivalent expression.
$$
\left(5^{4} \cdot b^{-10}\right)^{-6}=?
$$

Choose 1 answer:
(A) $5^{4} \cdot b^{60}$
(B) $5^{24} \cdot b^{60}$
(c) $\frac{b^{60}}{5^{24}}$

Question

Select the equivalent expression.
$$
\left(5^{4} \cdot b^{-10}\right)^{-6}=?
$$

Choose 1 answer:
(A) $5^{4} \cdot b^{60}$
(B) $5^{24} \cdot b^{60}$
(c) $\frac{b^{60}}{5^{24}}$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ We start with the given expression: $\left(5^{4} \cdot b^{-10}\right)^{-6}$ ‖ ‖ step 2 ⋮ Apply the negative exponent rule: $\left(5^{4} \cdot b^{-10}\right)^{-6} = \frac{1}{\left(5^{4} \cdot b^{-10}\right)^{6}}$ ‖ ‖ step 3 ⋮ Simplify the exponent: $\left(5^{4} \cdot b^{-10}\right)^{6} = 5^{4 \cdot 6} \cdot b^{-10 \cdot 6} = 5^{24} \cdot b^{-60}$ ‖ ‖ step 4 ⋮ Combine the results: $\frac{1}{5^{24} \cdot b^{-60}} = \frac{b^{60}}{5^{24}}$ ‖ ***C*** ∻Key Concept∻ ⚹Negative Exponent Rule⚹ ∻Explanation∻ ⚹When an expression with a negative exponent is simplified, it is equivalent to the reciprocal of the expression with a positive exponent.⚹◊What is the simplified expression for $(5^{4} \cdot b^{-10})^{-6}$ in terms of $b$?⍭ Generate me a similar question◊

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