To simplify the given expression [tex]\( x^{\frac{1}{5}} + y^{\frac{5}{5}} \)[/tex] using radicals and integer exponents, follow these steps:
### Step 1: Simplify Exponents
1. Rewrite [tex]\( y^{\frac{5}{5}} \)[/tex]:
Notice that [tex]\(\frac{5}{5} = 1\)[/tex]. Therefore,
[tex]\[ y^{\frac{5}{5}} = y^{1} = y \][/tex]
2. Rewrite [tex]\( x^{\frac{1}{5}} \)[/tex]:
Rewrite the fractional exponent as a radical. The expression [tex]\( x^{\frac{1}{5}} \)[/tex] can be expressed as the 5th root of [tex]\( x \)[/tex]:
[tex]\[ x^{\frac{1}{5}} = \sqrt[5]{x} \][/tex]
### Step 2: Combine Radicals and Integers
After rewriting both terms, the expression simplifies to:
[tex]\[
\sqrt[5]{x} + y
\][/tex]
### Final Answer
Thus, the simplified form of [tex]\( x^{\frac{1}{5}} + y^{\frac{5}{5}} \)[/tex] using radicals and integer exponents is:
[tex]\[
\boxed{\sqrt[5]{x} + y}
\][/tex]
