Simplify (16x)^(3/2)

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

Step 1

Simplify the expression.

Apply the product rule to $16 x$ .

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

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

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

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

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

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

$64 x^{\frac{3}{2}}$