Find g(h(x)) g(x)=(2x)^3 and h(x)=( cube root of x)/2

$g (x) = {(2 x)}^{3}$ and $h (x) = \frac{\sqrt[3]{x}}{2}$

Set up the composite result function.

$g (h (x))$

Evaluate $g (\frac{\sqrt[3]{x}}{2})$ by substituting in the value of $h$ into $g$ .

$g (\frac{\sqrt[3]{x}}{2}) = {(2 (\frac{\sqrt[3]{x}}{2}))}^{3}$

Cancel the common factor of $2$ .

Cancel the common factor.

$g (\frac{\sqrt[3]{x}}{2}) = {(2 (\frac{\sqrt[3]{x}}{2}))}^{3}$

Rewrite the expression.

$g (\frac{\sqrt[3]{x}}{2}) = {\sqrt[3]{x}}^{3}$

Rewrite ${\sqrt[3]{x}}^{3}$ as $x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x}$ as $x^{\frac{1}{3}}$ .

$g (\frac{\sqrt[3]{x}}{2}) = {(x^{\frac{1}{3}})}^{3}$

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

$g (\frac{\sqrt[3]{x}}{2}) = x^{\frac{1}{3} \cdot 3}$

Combine $\frac{1}{3}$ and $3$ .

$g (\frac{\sqrt[3]{x}}{2}) = x^{\frac{3}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$g (\frac{\sqrt[3]{x}}{2}) = x^{\frac{3}{3}}$

Rewrite the expression.

$g (\frac{\sqrt[3]{x}}{2}) = x$

Simplify.

$g (\frac{\sqrt[3]{x}}{2}) = x$