Simplify (125x^9y^6)^(1/3)

${(125 x^{9} y^{6})}^{\frac{1}{3}}$

Step 1

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

Apply the product rule to $125 x^{9} y^{6}$ .

${(125 x^{9})}^{\frac{1}{3}} {(y^{6})}^{\frac{1}{3}}$

Apply the product rule to $125 x^{9}$ .

$125^{\frac{1}{3}} {(x^{9})}^{\frac{1}{3}} {(y^{6})}^{\frac{1}{3}}$

Step 2

Simplify the expression.

Rewrite $125$ as $5^{3}$ .

${(5^{3})}^{\frac{1}{3}} {(x^{9})}^{\frac{1}{3}} {(y^{6})}^{\frac{1}{3}}$

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

$5^{3 (\frac{1}{3})} {(x^{9})}^{\frac{1}{3}} {(y^{6})}^{\frac{1}{3}}$

Step 3

Cancel the common factor of $3$ .

Cancel the common factor.

$5^{3 (\frac{1}{3})} {(x^{9})}^{\frac{1}{3}} {(y^{6})}^{\frac{1}{3}}$

Rewrite the expression.

$5^{1} {(x^{9})}^{\frac{1}{3}} {(y^{6})}^{\frac{1}{3}}$

Step 4

Evaluate the exponent.

$5 {(x^{9})}^{\frac{1}{3}} {(y^{6})}^{\frac{1}{3}}$

Step 5

Multiply the exponents in ${(x^{9})}^{\frac{1}{3}}$ .

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

$5 x^{9 (\frac{1}{3})} {(y^{6})}^{\frac{1}{3}}$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$5 x^{3 (3) \frac{1}{3}} {(y^{6})}^{\frac{1}{3}}$

Cancel the common factor.

$5 x^{3 \cdot 3 \frac{1}{3}} {(y^{6})}^{\frac{1}{3}}$

Rewrite the expression.

$5 x^{3} {(y^{6})}^{\frac{1}{3}}$

Step 6

Multiply the exponents in ${(y^{6})}^{\frac{1}{3}}$ .

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

$5 x^{3} y^{6 (\frac{1}{3})}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$5 x^{3} y^{2}$