Question

simplify. express your answer using positive exponents. $\frac{6pq^{2}}{p^{9}q^{5}}$

Explanation:

Step1: Use exponent - division rule

When dividing like - bases $a^m\div a^n=a^{m - n}$, for the $p$ terms: $\frac{p}{p^{9}}=p^{1-9}=p^{-8}$, and for the $q$ terms: $\frac{q^{2}}{q^{5}}=q^{2 - 5}=q^{-3}$. So the expression becomes $6\times p^{-8}\times q^{-3}$.

Step2: Rewrite with positive exponents

Using the rule $a^{-n}=\frac{1}{a^{n}}$, we rewrite $p^{-8}$ as $\frac{1}{p^{8}}$ and $q^{-3}$ as $\frac{1}{q^{3}}$. Then $6\times p^{-8}\times q^{-3}=\frac{6}{p^{8}q^{3}}$.

Answer:

$\frac{6}{p^{8}q^{3}}$