Simplify the Radical Expression (3p^3q)^(3/4)

${(3 p^{3} q)}^{\frac{3}{4}}$

Step 1

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

Apply the product rule to $3 p^{3} q$ .

${(3 p^{3})}^{\frac{3}{4}} q^{\frac{3}{4}}$

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

$3^{\frac{3}{4}} {(p^{3})}^{\frac{3}{4}} q^{\frac{3}{4}}$

Step 2

Multiply the exponents in ${(p^{3})}^{\frac{3}{4}}$ .

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

$3^{\frac{3}{4}} p^{3 (\frac{3}{4})} q^{\frac{3}{4}}$

Multiply $3 (\frac{3}{4})$ .

Combine $3$ and $\frac{3}{4}$ .

$3^{\frac{3}{4}} p^{\frac{3 \cdot 3}{4}} q^{\frac{3}{4}}$

Multiply $3$ by $3$ .

$3^{\frac{3}{4}} p^{\frac{9}{4}} q^{\frac{3}{4}}$