Simplify the Radical Expression (x^27y)^(1/3)

${(x^{27} y)}^{\frac{1}{3}}$

Step 1

Apply the product rule to $x^{27} y$ .

${(x^{27})}^{\frac{1}{3}} y^{\frac{1}{3}}$

Step 2

Multiply the exponents in ${(x^{27})}^{\frac{1}{3}}$ .

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

$x^{27 (\frac{1}{3})} y^{\frac{1}{3}}$

Cancel the common factor of $3$ .

Factor $3$ out of $27$ .

$x^{3 (9) \frac{1}{3}} y^{\frac{1}{3}}$

Cancel the common factor.

$x^{3 \cdot 9 \frac{1}{3}} y^{\frac{1}{3}}$

Rewrite the expression.

$x^{9} y^{\frac{1}{3}}$