Simplify ((2x^4)/3)^3

${(\frac{2 x^{4}}{3})}^{3}$

Step 1

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

Apply the product rule to $\frac{2 x^{4}}{3}$ .

$\frac{{(2 x^{4})}^{3}}{3^{3}}$

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

$\frac{2^{3} {(x^{4})}^{3}}{3^{3}}$

Step 2

Simplify the numerator.

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

$\frac{8 {(x^{4})}^{3}}{3^{3}}$

Multiply the exponents in ${(x^{4})}^{3}$ .

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

$\frac{8 x^{4 \cdot 3}}{3^{3}}$

Multiply $4$ by $3$ .

$\frac{8 x^{12}}{3^{3}}$

Step 3

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

$\frac{8 x^{12}}{27}$