Question

1. $(-3p^{4}q^{-3})^{2}(4p^{-5}q^{7})$

Explanation:

Step1: Apply power of a product rule

First, we apply the power of a product rule \((ab)^n = a^n b^n\) and the power of a power rule \((a^m)^n = a^{mn}\) to \((-3p^4q^{-3})^2\).

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Step2: Multiply with the second term

Now we multiply \(9p^{8}q^{-6}\) with \(4p^{-5}q^{7}\). When multiplying terms with the same base, we add the exponents (\(a^m \cdot a^n = a^{m + n}\)) and multiply the coefficients.

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Answer:

\(36p^{3}q\)