Question

simplify. express your answer using positive exponents.
$\frac{8fg^{-1}}{4f^{-1}g^{2}}$

Explanation:

Step1: Divide the coefficients

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

Step2: Apply exponent - rule for $f$ terms

$\frac{f}{f^{-1}}=f^{1-(-1)} = f^{2}$

Step3: Apply exponent - rule for $g$ terms

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

Step4: Combine the results

$2\times f^{2}\times\frac{1}{g^{3}}=\frac{2f^{2}}{g^{3}}$

Answer:

$\frac{2f^{2}}{g^{3}}$