Simplify (5x^(2/3)y^(7/5))^(1/7)

${(5 x^{\frac{2}{3}} y^{\frac{7}{5}})}^{\frac{1}{7}}$

Step 1

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

Apply the product rule to $5 x^{\frac{2}{3}} y^{\frac{7}{5}}$ .

${(5 x^{\frac{2}{3}})}^{\frac{1}{7}} {(y^{\frac{7}{5}})}^{\frac{1}{7}}$

Apply the product rule to $5 x^{\frac{2}{3}}$ .

$5^{\frac{1}{7}} {(x^{\frac{2}{3}})}^{\frac{1}{7}} {(y^{\frac{7}{5}})}^{\frac{1}{7}}$

Step 2

Multiply the exponents in ${(x^{\frac{2}{3}})}^{\frac{1}{7}}$ .

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

$5^{\frac{1}{7}} x^{\frac{2}{3} \cdot \frac{1}{7}} {(y^{\frac{7}{5}})}^{\frac{1}{7}}$

Multiply $\frac{2}{3} \cdot \frac{1}{7}$ .

Multiply $\frac{2}{3}$ by $\frac{1}{7}$ .

$5^{\frac{1}{7}} x^{\frac{2}{3 \cdot 7}} {(y^{\frac{7}{5}})}^{\frac{1}{7}}$

Multiply $3$ by $7$ .

$5^{\frac{1}{7}} x^{\frac{2}{21}} {(y^{\frac{7}{5}})}^{\frac{1}{7}}$

Step 3

Multiply the exponents in ${(y^{\frac{7}{5}})}^{\frac{1}{7}}$ .

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

$5^{\frac{1}{7}} x^{\frac{2}{21}} y^{\frac{7}{5} \cdot \frac{1}{7}}$

Cancel the common factor of $7$ .

Cancel the common factor.

$5^{\frac{1}{7}} x^{\frac{2}{21}} y^{\frac{7}{5} \cdot \frac{1}{7}}$

Rewrite the expression.

$5^{\frac{1}{7}} x^{\frac{2}{21}} y^{\frac{1}{5}}$