Simplify the Radical Expression (125x)^(4/3)

${(125 x)}^{\frac{4}{3}}$

Step 1

Apply the product rule to $125 x$ .

$125^{\frac{4}{3}} x^{\frac{4}{3}}$

Step 2

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

${(5^{3})}^{\frac{4}{3}} x^{\frac{4}{3}}$

Step 3

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

$5^{3 (\frac{4}{3})} x^{\frac{4}{3}}$

Step 4

Cancel the common factor of $3$ .

Cancel the common factor.

$5^{3 (\frac{4}{3})} x^{\frac{4}{3}}$

Rewrite the expression.

$5^{4} x^{\frac{4}{3}}$

Step 5

Raise $5$ to the power of $4$ .

$625 x^{\frac{4}{3}}$