Question

simplify. express your answer using positive exponents.
$\frac{2q^{6}r^{9}s}{2q^{9}r^{8}s}$

Explanation:

Step1: Divide the coefficients

$\frac{2}{2}=1$

Step2: Use the quotient - rule of exponents for $q$

$\frac{q^{6}}{q^{9}}=q^{6 - 9}=q^{- 3}=\frac{1}{q^{3}}$

Step3: Use the quotient - rule of exponents for $r$

$\frac{r^{9}}{r^{8}}=r^{9 - 8}=r^{1}=r$

Step4: Divide the $s$ terms

$\frac{s}{s}=1$

Step5: Combine the results

$1\times\frac{1}{q^{3}}\times r\times1=\frac{r}{q^{3}}$

Answer:

$\frac{r}{q^{3}}$