Question

simplify. express your answer using positive exponents. $\frac{6p^{7}q^{-4}}{3p^{0}q}$

Explanation:

Step1: Simplify the coefficient

Divide 6 by 3: $\frac{6}{3}=2$.

Step2: Use exponent - rule for $p$ terms

According to the rule $\frac{a^m}{a^n}=a^{m - n}$, for $p$ terms $\frac{p^7}{p^0}$, since $p^0 = 1$, we have $p^{7-0}=p^7$.

Step3: Use exponent - rule for $q$ terms

For $\frac{q^{-4}}{q^1}$, using $\frac{a^m}{a^n}=a^{m - n}$, we get $q^{-4 - 1}=q^{-5}$. Then, using $a^{-n}=\frac{1}{a^n}$, we rewrite $q^{-5}$ as $\frac{1}{q^5}$.

Step4: Combine the results

Multiply the simplified coefficient and the $p$ and $q$ terms: $2\times p^7\times\frac{1}{q^5}=\frac{2p^7}{q^5}$.

Answer:

$\frac{2p^7}{q^5}$