Question

Select the equivalent expression.
\[\left(a^{-7}\cdot b^{-2}\right)^{-9}=?\]
Choose 1 answer:
Choose 1 answer:
(Choice A)

\[\dfrac{a^{63}}{b^{18}}\]
A

\[\dfrac{a^{63}}{b^{18}}\]
(Choice B)
\[a^{63}\cdot b^{18}\]
B
\[a^{63}\cdot b^{18}\]
(Choice C)

\[\dfrac{b^{18}}{a^{63}}\]
C

\[\dfrac{b^{18}}{a^{63}}\]

Answer 1

To simplify the expression \(\left(a^{-7}\cdot b^{-2}\right)^{-9}\), we can use the property of exponents that states \((x^m)^n = x^{m \cdot n}\).

1. Start with the expression:
\[
\left(a^{-7}\cdot b^{-2}\right)^{-9}
\]

2. Apply the negative exponent:
\[
a^{-7 \cdot (-9)} \cdot b^{-2 \cdot (-9)}
\]

3. This simplifies to:
\[
a^{63} \cdot b^{18}
\]

Thus, the equivalent expression is:
\[
a^{63} \cdot b^{18}
\]

From the provided options, the correct choice is:

**B) \(a^{63} \cdot b^{18}\)**.