Question

Math

Posted about 1 month ago

```
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) $\frac{b^{60}}{5^{24}}$
```

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Answer from Sia

Posted about 1 month ago

Solution by Steps

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.

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