Question

$(n^{6}p^{-8}q^{5})^{-5}$

Explanation:

Step1: Apply the power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). For the expression \((n^{6}p^{-8}q^{5})^{-5}\), we apply this rule to each factor inside the parentheses:
\[
(n^{6}p^{-8}q^{5})^{-5}=n^{6\times(-5)}p^{-8\times(-5)}q^{5\times(-5)}
\]

Step2: Simplify the exponents

Now we calculate each exponent:

• For the \(n\) term: \(6\times(-5)= - 30\), so we have \(n^{-30}\)
• For the \(p\) term: \(-8\times(-5) = 40\), so we have \(p^{40}\)
• For the \(q\) term: \(5\times(-5)=-25\), so we have \(q^{-25}\)

We can also rewrite negative exponents as positive exponents in the denominator (using the rule \(a^{-n}=\frac{1}{a^{n}}\)). So \(n^{-30}=\frac{1}{n^{30}}\) and \(q^{-25}=\frac{1}{q^{25}}\). Combining these, the expression becomes:
\[
\frac{p^{40}}{n^{30}q^{25}}
\]

Answer:

\(\frac{p^{40}}{n^{30}q^{25}}\) (or \(n^{-30}p^{40}q^{-25}\) depending on the form required)