Simplify the Radical Expression (4x^6)^(3/2)

${(4 x^{6})}^{\frac{3}{2}}$

Step 1

Apply the product rule to $4 x^{6}$ .

$4^{\frac{3}{2}} {(x^{6})}^{\frac{3}{2}}$

Step 2

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

${(2^{2})}^{\frac{3}{2}} {(x^{6})}^{\frac{3}{2}}$

Step 3

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

$2^{2 (\frac{3}{2})} {(x^{6})}^{\frac{3}{2}}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$2^{2 (\frac{3}{2})} {(x^{6})}^{\frac{3}{2}}$

Rewrite the expression.

$2^{3} {(x^{6})}^{\frac{3}{2}}$

Step 5

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

$8 {(x^{6})}^{\frac{3}{2}}$

Step 6

Multiply the exponents in ${(x^{6})}^{\frac{3}{2}}$ .

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

$8 x^{6 (\frac{3}{2})}$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$8 x^{2 (3) \frac{3}{2}}$

Cancel the common factor.

$8 x^{2 \cdot 3 \frac{3}{2}}$

Rewrite the expression.

$8 x^{3 \cdot 3}$

Multiply $3$ by $3$ .

$8 x^{9}$