Simplify (f^-3g^5h^8)^-3

${(f^{- 3} g^{5} h^{8})}^{- 3}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{1}{f^{3}} g^{5} h^{8})}^{- 3}$

Step 2

Combine $\frac{1}{f^{3}}$ and $g^{5}$ .

${(\frac{g^{5}}{f^{3}} h^{8})}^{- 3}$

Step 3

Combine $\frac{g^{5}}{f^{3}}$ and $h^{8}$ .

${(\frac{g^{5} h^{8}}{f^{3}})}^{- 3}$

Step 4

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{f^{3}}{g^{5} h^{8}})}^{3}$

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{f^{3}}{g^{5} h^{8}}$ .

$\frac{{(f^{3})}^{3}}{{(g^{5} h^{8})}^{3}}$

Apply the product rule to $g^{5} h^{8}$ .

$\frac{{(f^{3})}^{3}}{{(g^{5})}^{3} {(h^{8})}^{3}}$

Step 6

Multiply the exponents in ${(f^{3})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{f^{3 \cdot 3}}{{(g^{5})}^{3} {(h^{8})}^{3}}$

Multiply $3$ by $3$ .

$\frac{f^{9}}{{(g^{5})}^{3} {(h^{8})}^{3}}$

Step 7

Simplify the denominator.

Multiply the exponents in ${(g^{5})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{f^{9}}{g^{5 \cdot 3} {(h^{8})}^{3}}$

Multiply $5$ by $3$ .

$\frac{f^{9}}{g^{15} {(h^{8})}^{3}}$

Multiply the exponents in ${(h^{8})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{f^{9}}{g^{15} h^{8 \cdot 3}}$

Multiply $8$ by $3$ .

$\frac{f^{9}}{g^{15} h^{24}}$