Question

simplify. express your answer using positive exponents.
$\frac{4u^{9}v^{-9}}{2u^{8}v}$

Explanation:

Step1: Divide the coefficients

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

Step2: Use the quotient - rule for exponents with the same base ($a^m\div a^n=a^{m - n}$) for $u$ terms

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

Step3: Use the quotient - rule for exponents with the same base for $v$ terms

$\frac{v^{-9}}{v^{1}}=v^{-9-1}=v^{-10}=\frac{1}{v^{10}}$

Step4: Combine the results

$2\times u\times\frac{1}{v^{10}}=\frac{2u}{v^{10}}$

Answer:

$\frac{2u}{v^{10}}$