Select the equivalent expression.

Question

\[\left(a^{-7}\cdot b^{-2}\right)^{-9}=?\]
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) \(a^{63} \cdot b^{18}\).