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

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

Step 1

Apply the product rule to $27 x$ .

$27^{\frac{1}{3}} x^{\frac{1}{3}}$

Step 2

Rewrite $27$ as $3^{3}$ .

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

Step 3

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

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

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

Evaluate the exponent.

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