Simplify ((x^(2/5)*x^(4/5))/(x^(2/5)))^(1/2)

${(\frac{x^{\frac{2}{5}} \cdot x^{\frac{4}{5}}}{x^{\frac{2}{5}}})}^{\frac{1}{2}}$

Multiply $x^{\frac{2}{5}}$ by $x^{\frac{4}{5}}$ by adding the exponents.

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

${(\frac{x^{\frac{2}{5} + \frac{4}{5}}}{x^{\frac{2}{5}}})}^{\frac{1}{2}}$

Combine the numerators over the common denominator.

${(\frac{x^{\frac{2 + 4}{5}}}{x^{\frac{2}{5}}})}^{\frac{1}{2}}$

Add $2$ and $4$ .

${(\frac{x^{\frac{6}{5}}}{x^{\frac{2}{5}}})}^{\frac{1}{2}}$

Move $x^{\frac{2}{5}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

${(x^{\frac{6}{5}} x^{- \frac{2}{5}})}^{\frac{1}{2}}$

Multiply $x^{\frac{6}{5}}$ by $x^{- \frac{2}{5}}$ by adding the exponents.

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

${(x^{\frac{6}{5} - \frac{2}{5}})}^{\frac{1}{2}}$

Combine the numerators over the common denominator.

${(x^{\frac{6 - 2}{5}})}^{\frac{1}{2}}$

Subtract $2$ from $6$ .

${(x^{\frac{4}{5}})}^{\frac{1}{2}}$

Multiply the exponents in ${(x^{\frac{4}{5}})}^{\frac{1}{2}}$ .

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

$x^{\frac{4}{5} \cdot \frac{1}{2}}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$x^{\frac{2 (2)}{5} \cdot \frac{1}{2}}$

Cancel the common factor.

$x^{\frac{2 \cdot 2}{5} \cdot \frac{1}{2}}$

Rewrite the expression.

$x^{\frac{2}{5}}$