Explain rational exponents as extensions of integer exponent rules and as radical notation.
Rewrite a rational exponent in radical notation
Problem
Rewrite \(a^{3/2}\) in radical notation. Use the denominator as the root index and the numerator as the power.
Big Picture
What this problem is really about
A rational exponent assigns different jobs to its numerator and denominator. We’ll use the denominator as the root index, use the numerator as the power, build the radical without swapping those roles, and convert it back with a power of a power to verify.
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