Simplify (16^(3/2))^(1/2)

${(16^{\frac{3}{2}})}^{\frac{1}{2}}$

Step 1

Simplify the expression.

Multiply the exponents in ${(16^{\frac{3}{2}})}^{\frac{1}{2}}$ .

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

$16^{\frac{3}{2} \cdot \frac{1}{2}}$

Multiply $\frac{3}{2} \cdot \frac{1}{2}$ .

Multiply $\frac{3}{2}$ by $\frac{1}{2}$ .

$16^{\frac{3}{2 \cdot 2}}$

Multiply $2$ by $2$ .

$16^{\frac{3}{4}}$

Rewrite $16$ as $2^{4}$ .

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

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

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

Step 2

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

$2^{3}$

Step 3

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

$8$