Simplify (216r^9)^(1/3)

${(216 r^{9})}^{\frac{1}{3}}$

Step 1

Simplify the expression.

Apply the product rule to $216 r^{9}$ .

$216^{\frac{1}{3}} {(r^{9})}^{\frac{1}{3}}$

Rewrite $216$ as $6^{3}$ .

${(6^{3})}^{\frac{1}{3}} {(r^{9})}^{\frac{1}{3}}$

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

$6^{3 (\frac{1}{3})} {(r^{9})}^{\frac{1}{3}}$

Step 2

Cancel the common factor of $3$ .

Cancel the common factor.

$6^{3 (\frac{1}{3})} {(r^{9})}^{\frac{1}{3}}$

Rewrite the expression.

$6^{1} {(r^{9})}^{\frac{1}{3}}$

Step 3

Simplify the expression.

Evaluate the exponent.

$6 {(r^{9})}^{\frac{1}{3}}$

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

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

$6 r^{9 (\frac{1}{3})}$

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$6 r^{3 (3) \frac{1}{3}}$

Cancel the common factor.

$6 r^{3 \cdot 3 \frac{1}{3}}$

Rewrite the expression.

$6 r^{3}$