Question

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

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So, for \((n^{9}p^{-4}q^{3})^{5}\), we apply this rule to each factor: \(n^{9\times5}p^{-4\times5}q^{3\times5}\).

Step2: Multiply the exponents

Calculate the exponents: \(9\times5 = 45\), \(-4\times5=-20\), and \(3\times5 = 15\). So we get \(n^{45}p^{-20}q^{15}\).

Answer:

\(n^{45}p^{-20}q^{15}\)