Question

simplify. express your answer using exponents. \\((n^{4}p^{-5}q^{-9})^{-3}\\)

Explanation:

Step1: Apply power of a product rule

For a product \((abc)^n = a^n b^n c^n\), so \((n^{4}p^{-5}q^{-9})^{-3}=n^{4\times(-3)}p^{-5\times(-3)}q^{-9\times(-3)}\)

Step2: Multiply the exponents

Calculate each exponent: \(4\times(-3)= - 12\), \(-5\times(-3)=15\), \(-9\times(-3)=27\)
So we get \(n^{-12}p^{15}q^{27}\)
But we usually write with positive exponents for negative exponents in the numerator, so \(n^{-12}=\frac{1}{n^{12}}\), but if we can have negative exponents, or we can rewrite as \(\frac{p^{15}q^{27}}{n^{12}}\) or keep negative exponents as \(n^{- 12}p^{15}q^{27}\)

Answer:

\(n^{-12}p^{15}q^{27}\) (or \(\frac{p^{15}q^{27}}{n^{12}}\))