Simplify (5^2b^3)^(2/3)

${(5^{2} b^{3})}^{\frac{2}{3}}$

Step 1

Raise $5$ to the power of $2$ .

${(25 b^{3})}^{\frac{2}{3}}$

Step 2

Apply the product rule to $25 b^{3}$ .

$25^{\frac{2}{3}} {(b^{3})}^{\frac{2}{3}}$

Step 3

Multiply the exponents in ${(b^{3})}^{\frac{2}{3}}$ .

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

$25^{\frac{2}{3}} b^{3 (\frac{2}{3})}$

Cancel the common factor of $3$ .

Cancel the common factor.

$25^{\frac{2}{3}} b^{3 (\frac{2}{3})}$

Rewrite the expression.

$25^{\frac{2}{3}} b^{2}$

Step 4

Reorder factors in $25^{\frac{2}{3}} b^{2}$ .

$b^{2} \cdot 25^{\frac{2}{3}}$