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Posted about 1 month ago

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

Choose 1 answer:
(A) 54b605^{4} \cdot b^{60}
(B) 524b605^{24} \cdot b^{60}
(c) b60524\frac{b^{60}}{5^{24}}
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Answer from Sia
Posted about 1 month ago
Solution by Steps
step 2
Apply the negative exponent rule: (54b10)6=1(54b10)6\left(5^{4} \cdot b^{-10}\right)^{-6} = \frac{1}{\left(5^{4} \cdot b^{-10}\right)^{6}}
step 3
Simplify the exponent: (54b10)6=546b106=524b60\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: 1524b60=b60524\frac{1}{5^{24} \cdot b^{-60}} = \frac{b^{60}}{5^{24}}
Key Concept
Negative Exponent Rule
When an expression with a negative exponent is simplified, it is equivalent to the reciprocal of the expression with a positive exponent.

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