Evaluate (81x^7y^11)^(1/3)

${(81 x^{7} y^{11})}^{\frac{1}{3}}$

Step 1

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

Apply the product rule to $81 x^{7} y^{11}$ .

${(81 x^{7})}^{\frac{1}{3}} {(y^{11})}^{\frac{1}{3}}$

Apply the product rule to $81 x^{7}$ .

$81^{\frac{1}{3}} {(x^{7})}^{\frac{1}{3}} {(y^{11})}^{\frac{1}{3}}$

Step 2

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

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

$81^{\frac{1}{3}} x^{7 (\frac{1}{3})} {(y^{11})}^{\frac{1}{3}}$

Combine $7$ and $\frac{1}{3}$ .

$81^{\frac{1}{3}} x^{\frac{7}{3}} {(y^{11})}^{\frac{1}{3}}$

Step 3

Multiply the exponents in ${(y^{11})}^{\frac{1}{3}}$ .

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

$81^{\frac{1}{3}} x^{\frac{7}{3}} y^{11 (\frac{1}{3})}$

Combine $11$ and $\frac{1}{3}$ .

$81^{\frac{1}{3}} x^{\frac{7}{3}} y^{\frac{11}{3}}$