Simplify (p^6q^(3/2))^(1/3)

${(p^{6} q^{\frac{3}{2}})}^{\frac{1}{3}}$

Step 1

Apply the product rule to $p^{6} q^{\frac{3}{2}}$ .

${(p^{6})}^{\frac{1}{3}} {(q^{\frac{3}{2}})}^{\frac{1}{3}}$

Step 2

Multiply the exponents in ${(p^{6})}^{\frac{1}{3}}$ .

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

$p^{6 (\frac{1}{3})} {(q^{\frac{3}{2}})}^{\frac{1}{3}}$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$p^{3 (2) \frac{1}{3}} {(q^{\frac{3}{2}})}^{\frac{1}{3}}$

Cancel the common factor.

$p^{3 \cdot 2 \frac{1}{3}} {(q^{\frac{3}{2}})}^{\frac{1}{3}}$

Rewrite the expression.

$p^{2} {(q^{\frac{3}{2}})}^{\frac{1}{3}}$

Step 3

Multiply the exponents in ${(q^{\frac{3}{2}})}^{\frac{1}{3}}$ .

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

$p^{2} q^{\frac{3}{2} \cdot \frac{1}{3}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$p^{2} q^{\frac{3}{2} \cdot \frac{1}{3}}$

Rewrite the expression.

$p^{2} q^{\frac{1}{2}}$