Question

simplify. express your answer using positive exponents.
$\frac{8uv^{6}w^{-7}}{2u^{-8}v^{5}w^{-1}}$

Explanation:

Step1: Divide the coefficients

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

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

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

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

$\frac{v^{6}}{v^{5}}=v^{6 - 5}=v^{1}=v$

Step4: Use the quotient - rule of exponents for $w$

$\frac{w^{-7}}{w^{-1}}=w^{-7-(-1)}=w^{-6}=\frac{1}{w^{6}}$

Step5: Combine the results

$4u^{9}v\times\frac{1}{w^{6}}=\frac{4u^{9}v}{w^{6}}$

Answer:

$\frac{4u^{9}v}{w^{6}}$