Simplify (x^(4/3)x^(2/3))^(1/3)

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

Step 1

Multiply $x^{\frac{4}{3}}$ by $x^{\frac{2}{3}}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(x^{\frac{4}{3} + \frac{2}{3}})}^{\frac{1}{3}}$

Combine the numerators over the common denominator.

${(x^{\frac{4 + 2}{3}})}^{\frac{1}{3}}$

Add $4$ and $2$ .

${(x^{\frac{6}{3}})}^{\frac{1}{3}}$

Divide $6$ by $3$ .

${(x^{2})}^{\frac{1}{3}}$

Step 2

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

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

$x^{2 (\frac{1}{3})}$

Combine $2$ and $\frac{1}{3}$ .

$x^{\frac{2}{3}}$