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

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

Step 1

Simplify the expression.

Apply the product rule to $16 x^{2}$ .

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

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

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

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

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

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Simplify the expression.

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$64 x^{3}$