Simplify the Radical Expression (x^10)^(1/5)+(x^4)^(1/2)

${(x^{10})}^{\frac{1}{5}} + {(x^{4})}^{\frac{1}{2}}$

Step 1

Simplify each term.

Multiply the exponents in ${(x^{10})}^{\frac{1}{5}}$ .

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

$x^{10 (\frac{1}{5})} + {(x^{4})}^{\frac{1}{2}}$

Cancel the common factor of $5$ .

Factor $5$ out of $10$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x^{2} + x^{2}$

Step 2

Add $x^{2}$ and $x^{2}$ .

$2 x^{2}$