Question

simplify. express your answer using positive exponents. $\frac{8s^{9}t^{5}u^{5}}{2s^{9}t^{7}u^{8}}$

Explanation:

Step1: Divide the coefficients

$\frac{8}{2}=4$

Step2: Use the quotient - rule for exponents $a^m\div a^n=a^{m - n}$ for $s$ terms

$\frac{s^{9}}{s^{9}}=s^{9 - 9}=s^{0}=1$

Step3: Use the quotient - rule for exponents for $t$ terms

$\frac{t^{5}}{t^{7}}=t^{5 - 7}=t^{- 2}=\frac{1}{t^{2}}$

Step4: Use the quotient - rule for exponents for $u$ terms

$\frac{u^{5}}{u^{8}}=u^{5 - 8}=u^{-3}=\frac{1}{u^{3}}$

Step5: Combine the results

$4\times1\times\frac{1}{t^{2}}\times\frac{1}{u^{3}}=\frac{4}{t^{2}u^{3}}$

Answer:

$\frac{4}{t^{2}u^{3}}$