Question

simplify. express your answer using positive exponents.
$\frac{9fg^{5}h}{3f^{4}g^{8}h^{5}}$

Explanation:

Step1: Simplify the coefficient

Divide 9 by 3: $\frac{9}{3}=3$.

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

For $f$, we have $\frac{f}{f^{4}}=f^{1 - 4}=f^{-3}=\frac{1}{f^{3}}$ according to the rule $\frac{a^{m}}{a^{n}}=a^{m - n}$.

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

For $g$, $\frac{g^{5}}{g^{8}}=g^{5 - 8}=g^{-3}=\frac{1}{g^{3}}$ using $\frac{a^{m}}{a^{n}}=a^{m - n}$.

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

For $h$, $\frac{h}{h^{5}}=h^{1 - 5}=h^{-4}=\frac{1}{h^{4}}$ by $\frac{a^{m}}{a^{n}}=a^{m - n}$.

Step5: Combine the results

Multiply the simplified coefficient and the variable - terms: $3\times\frac{1}{f^{3}}\times\frac{1}{g^{3}}\times\frac{1}{h^{4}}=\frac{3}{f^{3}g^{3}h^{4}}$.

Answer:

$\frac{3}{f^{3}g^{3}h^{4}}$