Question

Select the equivalent expression.

\[\left(\dfrac{b^{7}}{4^{5}}\right)^{-3}=?\]
Choose 1 answer:
Choose 1 answer:
(Choice A)
\[{b^{-21}}\cdot{4^{-15}}\]
A
\[{b^{-21}}\cdot{4^{-15}}\]
(Choice B)

\[\dfrac{4^{15}}{b^{21}}\]
B

\[\dfrac{4^{15}}{b^{21}}\]
(Choice C)

\[\dfrac{b^{21}}{4^{15}}\]
C

\[\dfrac{b^{21}}{4^{15}}\]

Answer 1

To simplify the expression \(\left(\dfrac{b^{7}}{4^{5}}\right)^{-3}\), we can apply the property of exponents that states \((\frac{a}{b})^{-n} = \frac{b^n}{a^n}\) and also distribute the exponent to both the numerator and denominator.

Starting with the given expression:

\[
\left(\dfrac{b^{7}}{4^{5}}\right)^{-3}
\]

We apply the negative exponent:

\[
= \dfrac{4^{5 \cdot 3}}{b^{7 \cdot 3}} = \dfrac{4^{15}}{b^{21}}
\]

Now, we look at the choices we have:

- (Choice A): \[{b^{-21}}\cdot{4^{-15}}\]
- (Choice B): \[\dfrac{4^{15}}{b^{21}}\]
- (Choice C): \[\dfrac{b^{21}}{4^{15}}\]

The correct choice matches our result:

\[\dfrac{4^{15}}{b^{21}}\]

So the equivalent expression is:

**(Choice B) \(\dfrac{4^{15}}{b^{21}}\)**.