Simplify the Radical Expression (7x^3y^2)^(2/7)

${(7 x^{3} y^{2})}^{\frac{2}{7}}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $7 x^{3} y^{2}$ .

${(7 x^{3})}^{\frac{2}{7}} {(y^{2})}^{\frac{2}{7}}$

Apply the product rule to $7 x^{3}$ .

$7^{\frac{2}{7}} {(x^{3})}^{\frac{2}{7}} {(y^{2})}^{\frac{2}{7}}$

Step 2

Multiply the exponents in ${(x^{3})}^{\frac{2}{7}}$ .

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

$7^{\frac{2}{7}} x^{3 (\frac{2}{7})} {(y^{2})}^{\frac{2}{7}}$

Multiply $3 (\frac{2}{7})$ .

Combine $3$ and $\frac{2}{7}$ .

$7^{\frac{2}{7}} x^{\frac{3 \cdot 2}{7}} {(y^{2})}^{\frac{2}{7}}$

Multiply $3$ by $2$ .

$7^{\frac{2}{7}} x^{\frac{6}{7}} {(y^{2})}^{\frac{2}{7}}$

Step 3

Multiply the exponents in ${(y^{2})}^{\frac{2}{7}}$ .

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

$7^{\frac{2}{7}} x^{\frac{6}{7}} y^{2 (\frac{2}{7})}$

Multiply $2 (\frac{2}{7})$ .

Combine $2$ and $\frac{2}{7}$ .

$7^{\frac{2}{7}} x^{\frac{6}{7}} y^{\frac{2 \cdot 2}{7}}$

Multiply $2$ by $2$ .

$7^{\frac{2}{7}} x^{\frac{6}{7}} y^{\frac{4}{7}}$