Simplify (2a^(2/3)b^(1/4))^(1/3)

${(2 a^{\frac{2}{3}} b^{\frac{1}{4}})}^{\frac{1}{3}}$

Step 1

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

Apply the product rule to $2 a^{\frac{2}{3}} b^{\frac{1}{4}}$ .

${(2 a^{\frac{2}{3}})}^{\frac{1}{3}} {(b^{\frac{1}{4}})}^{\frac{1}{3}}$

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

$2^{\frac{1}{3}} {(a^{\frac{2}{3}})}^{\frac{1}{3}} {(b^{\frac{1}{4}})}^{\frac{1}{3}}$

Step 2

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

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

$2^{\frac{1}{3}} a^{\frac{2}{3} \cdot \frac{1}{3}} {(b^{\frac{1}{4}})}^{\frac{1}{3}}$

Multiply $\frac{2}{3} \cdot \frac{1}{3}$ .

Multiply $\frac{2}{3}$ by $\frac{1}{3}$ .

$2^{\frac{1}{3}} a^{\frac{2}{3 \cdot 3}} {(b^{\frac{1}{4}})}^{\frac{1}{3}}$

Multiply $3$ by $3$ .

$2^{\frac{1}{3}} a^{\frac{2}{9}} {(b^{\frac{1}{4}})}^{\frac{1}{3}}$

Step 3

Multiply the exponents in ${(b^{\frac{1}{4}})}^{\frac{1}{3}}$ .

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

$2^{\frac{1}{3}} a^{\frac{2}{9}} b^{\frac{1}{4} \cdot \frac{1}{3}}$

Multiply $\frac{1}{4} \cdot \frac{1}{3}$ .

Multiply $\frac{1}{4}$ by $\frac{1}{3}$ .

$2^{\frac{1}{3}} a^{\frac{2}{9}} b^{\frac{1}{4 \cdot 3}}$

Multiply $4$ by $3$ .

$2^{\frac{1}{3}} a^{\frac{2}{9}} b^{\frac{1}{12}}$