Explain rational exponents as extensions of integer exponent rules and as radical notation.
Rewrite an expression with exponent \(1/n\) in radical notation
Problem
Use \(a^{1/n}=\sqrt[n]{a}\) with \(n=2\) to rewrite \(a^{1/2}\) in radical notation.
Big Picture
What this problem is really about
In a unit-fraction exponent, the denominator becomes the radical’s index. We’ll identify that denominator, translate it to the corresponding root, apply the convention that a square-root index is omitted, and reverse the conversion to check the notation.
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