Question

simplify. express your answer using positive exponents. $\frac{5pq^{-1}r}{5p^{7}q^{-1}r^{-1}}$

Explanation:

Step1: Divide the coefficients

The coefficients are 5 and 5. $\frac{5}{5}=1$.

Step2: Use the quotient - rule for exponents ($\frac{a^m}{a^n}=a^{m - n}$) for $p$

For the $p$ terms, we have $\frac{p}{p^{7}}=p^{1-7}=p^{-6}$. Since we want positive exponents, $p^{-6}=\frac{1}{p^{6}}$.

Step3: Use the quotient - rule for exponents for $q$

For the $q$ terms, $\frac{q^{-1}}{q^{-1}}=q^{-1-(-1)}=q^{-1 + 1}=q^{0}=1$.

Step4: Use the quotient - rule for exponents for $r$

For the $r$ terms, $\frac{r}{r^{-1}}=r^{1-(-1)}=r^{2}$.

Step5: Combine the results

The simplified expression is $\frac{r^{2}}{p^{6}}$.

Answer:

$\frac{r^{2}}{p^{6}}$