Simplify ((2g^5)^3)/((4h^2)^3)

$\frac{{(2 g^{5})}^{3}}{{(4 h^{2})}^{3}}$

Step 1

Simplify the numerator.

Apply the product rule to $2 g^{5}$ .

$\frac{2^{3} {(g^{5})}^{3}}{{(4 h^{2})}^{3}}$

Raise $2$ to the power of $3$ .

$\frac{8 {(g^{5})}^{3}}{{(4 h^{2})}^{3}}$

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

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

$\frac{8 g^{5 \cdot 3}}{{(4 h^{2})}^{3}}$

Multiply $5$ by $3$ .

$\frac{8 g^{15}}{{(4 h^{2})}^{3}}$

Step 2

Simplify the denominator.

Apply the product rule to $4 h^{2}$ .

$\frac{8 g^{15}}{4^{3} {(h^{2})}^{3}}$

Raise $4$ to the power of $3$ .

$\frac{8 g^{15}}{64 {(h^{2})}^{3}}$

Multiply the exponents in ${(h^{2})}^{3}$ .

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

$\frac{8 g^{15}}{64 h^{2 \cdot 3}}$

Multiply $2$ by $3$ .

$\frac{8 g^{15}}{64 h^{6}}$

Step 3

Cancel the common factor of $8$ and $64$ .

Factor $8$ out of $8 g^{15}$ .

$\frac{8 (g^{15})}{64 h^{6}}$

Cancel the common factors.

Factor $8$ out of $64 h^{6}$ .

$\frac{8 (g^{15})}{8 (8 h^{6})}$

Cancel the common factor.

$\frac{8 g^{15}}{8 (8 h^{6})}$

Rewrite the expression.

$\frac{g^{15}}{8 h^{6}}$