Simplify the Radical Expression (x^16y^8)^(3/8)

${(x^{16} y^{8})}^{\frac{3}{8}}$

Step 1

Apply the product rule to $x^{16} y^{8}$ .

${(x^{16})}^{\frac{3}{8}} {(y^{8})}^{\frac{3}{8}}$

Step 2

Multiply the exponents in ${(x^{16})}^{\frac{3}{8}}$ .

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

$x^{16 (\frac{3}{8})} {(y^{8})}^{\frac{3}{8}}$

Cancel the common factor of $8$ .

Factor $8$ out of $16$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $2$ by $3$ .

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

Step 3

Multiply the exponents in ${(y^{8})}^{\frac{3}{8}}$ .

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

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

Cancel the common factor of $8$ .

Cancel the common factor.

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

Rewrite the expression.

$x^{6} y^{3}$