Explain rational exponents as extensions of integer exponent rules and as radical notation.
Reduce a rational exponent, then evaluate it exactly
Problem
Reduce the exponent \(2/6\) to lowest terms, then evaluate \(64^{2/6}\) exactly. State \(\text{both}~\text{the}~\text{reduced}~\text{exponential}~\text{form}~\text{and}~\text{its}~\text{value}\).
Big Picture
What this problem is really about
Reducing a rational exponent first can reveal a familiar exact root. We’ll divide numerator and denominator by their common factor, preserve the reduced exponential form, translate its denominator into a root index, and verify the exact value by raising the candidate back to that index.
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