simplify. express your answer using positive exponents.\n$\frac{4q^{3}r^{-4}s^{-7}}{4q^{2}r^{-1}s^{-8}}$

Explanation:

Step1: Divide the coefficients

$\frac{4}{4}=1$

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

$\frac{q^{3}}{q^{2}}=q^{3 - 2}=q^{1}=q$

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

$\frac{r^{- 4}}{r^{-1}}=r^{-4-(-1)}=r^{-4 + 1}=r^{-3}=\frac{1}{r^{3}}$

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

$\frac{s^{-7}}{s^{-8}}=s^{-7-(-8)}=s^{-7 + 8}=s^{1}=s$

Step5: Combine the results

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

Answer:

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