Evaluate 4(4)^(3/2)

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

Multiply $4$ by ${(4)}^{\frac{3}{2}}$ by adding the exponents.

Multiply $4$ by ${(4)}^{\frac{3}{2}}$ .

Raise $4$ to the power of $1$ .

$4^{1} {(4)}^{\frac{3}{2}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4^{1 + \frac{3}{2}}$

Write $1$ as a fraction with a common denominator.

$4^{\frac{2}{2} + \frac{3}{2}}$

Combine the numerators over the common denominator.

$4^{\frac{2 + 3}{2}}$

Add $2$ and $3$ .

$4^{\frac{5}{2}}$

Simplify the expression.

Rewrite $4$ as $2^{2}$ .

${(2^{2})}^{\frac{5}{2}}$

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

$2^{2 (\frac{5}{2})}$

Cancel the common factor of $2$ .

Cancel the common factor.

$2^{2 (\frac{5}{2})}$

Rewrite the expression.

$2^{5}$

Raise $2$ to the power of $5$ .

$32$