Question

select the equivalent expression. ((a^{-7} cdot b^{-2})^{-9} =?) choose 1 answer: a (\frac{b^{18}}{a^{63}}) b (\frac{a^{63}}{b^{18}}) c (a^{63} cdot b^{18})

Explanation:

Step1: Apply power of a product rule

$(x\cdot y)^n = x^n \cdot y^n$, so:
$$(a^{-7} \cdot b^{-2})^{-9} = (a^{-7})^{-9} \cdot (b^{-2})^{-9}$$

Step2: Apply power of a power rule

$(x^m)^n = x^{m\cdot n}$, calculate exponents:
$$(a^{-7})^{-9} = a^{(-7)\times(-9)} = a^{63}$$
$$(b^{-2})^{-9} = b^{(-2)\times(-9)} = b^{18}$$

Step3: Combine the results

Multiply the simplified terms:
$$a^{63} \cdot b^{18}$$

Answer:

C. $a^{63} \cdot b^{18}$