Simplify the Radical Expression (27x)^(5/3)

${(27 x)}^{\frac{5}{3}}$

Step 1

Apply the product rule to $27 x$ .

$27^{\frac{5}{3}} x^{\frac{5}{3}}$

Step 2

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

${(3^{3})}^{\frac{5}{3}} x^{\frac{5}{3}}$

Step 3

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

$3^{3 (\frac{5}{3})} x^{\frac{5}{3}}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$3^{3 (\frac{5}{3})} x^{\frac{5}{3}}$

Rewrite the expression.

$3^{5} x^{\frac{5}{3}}$

Step 5

Raise $3$ to the power of $5$ .

$243 x^{\frac{5}{3}}$