Simplify (p^3q^(1/2)r^(1/5))^(2/11)

${(p^{3} q^{\frac{1}{2}} r^{\frac{1}{5}})}^{\frac{2}{11}}$

Step 1

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

Apply the product rule to $p^{3} q^{\frac{1}{2}} r^{\frac{1}{5}}$ .

${(p^{3} q^{\frac{1}{2}})}^{\frac{2}{11}} {(r^{\frac{1}{5}})}^{\frac{2}{11}}$

Apply the product rule to $p^{3} q^{\frac{1}{2}}$ .

${(p^{3})}^{\frac{2}{11}} {(q^{\frac{1}{2}})}^{\frac{2}{11}} {(r^{\frac{1}{5}})}^{\frac{2}{11}}$

Step 2

Multiply the exponents in ${(p^{3})}^{\frac{2}{11}}$ .

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

$p^{3 (\frac{2}{11})} {(q^{\frac{1}{2}})}^{\frac{2}{11}} {(r^{\frac{1}{5}})}^{\frac{2}{11}}$

Multiply $3 (\frac{2}{11})$ .

Combine $3$ and $\frac{2}{11}$ .

$p^{\frac{3 \cdot 2}{11}} {(q^{\frac{1}{2}})}^{\frac{2}{11}} {(r^{\frac{1}{5}})}^{\frac{2}{11}}$

Multiply $3$ by $2$ .

$p^{\frac{6}{11}} {(q^{\frac{1}{2}})}^{\frac{2}{11}} {(r^{\frac{1}{5}})}^{\frac{2}{11}}$

Step 3

Multiply the exponents in ${(q^{\frac{1}{2}})}^{\frac{2}{11}}$ .

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

$p^{\frac{6}{11}} q^{\frac{1}{2} \cdot \frac{2}{11}} {(r^{\frac{1}{5}})}^{\frac{2}{11}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$p^{\frac{6}{11}} q^{\frac{1}{2} \cdot \frac{2}{11}} {(r^{\frac{1}{5}})}^{\frac{2}{11}}$

Rewrite the expression.

$p^{\frac{6}{11}} q^{\frac{1}{11}} {(r^{\frac{1}{5}})}^{\frac{2}{11}}$

Step 4

Multiply the exponents in ${(r^{\frac{1}{5}})}^{\frac{2}{11}}$ .

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

$p^{\frac{6}{11}} q^{\frac{1}{11}} r^{\frac{1}{5} \cdot \frac{2}{11}}$

Multiply $\frac{1}{5} \cdot \frac{2}{11}$ .

Multiply $\frac{1}{5}$ by $\frac{2}{11}$ .

$p^{\frac{6}{11}} q^{\frac{1}{11}} r^{\frac{2}{5 \cdot 11}}$

Multiply $5$ by $11$ .

$p^{\frac{6}{11}} q^{\frac{1}{11}} r^{\frac{2}{55}}$