Simplify the Radical Expression (3/(2p^2))^(2/3)

${(\frac{3}{2 p^{2}})}^{\frac{2}{3}}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{3}{2 p^{2}}$ .

$\frac{3^{\frac{2}{3}}}{{(2 p^{2})}^{\frac{2}{3}}}$

Apply the product rule to $2 p^{2}$ .

$\frac{3^{\frac{2}{3}}}{2^{\frac{2}{3}} {(p^{2})}^{\frac{2}{3}}}$

Step 2

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

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

$\frac{3^{\frac{2}{3}}}{2^{\frac{2}{3}} p^{2 (\frac{2}{3})}}$

Multiply $2 (\frac{2}{3})$ .

Combine $2$ and $\frac{2}{3}$ .

$\frac{3^{\frac{2}{3}}}{2^{\frac{2}{3}} p^{\frac{2 \cdot 2}{3}}}$

Multiply $2$ by $2$ .

$\frac{3^{\frac{2}{3}}}{2^{\frac{2}{3}} p^{\frac{4}{3}}}$