Explain rational exponents as extensions of integer exponent rules and as radical notation.
Evaluate powers with negative rational exponents by using roots and reciprocals
Problem
Evaluate \(16^{-1/2}\).
Big Picture
What this problem is really about
The negative sign on an exponent makes the entire positive power reciprocal. We’ll remove that sign by placing the power in the denominator, interpret the remaining fractional exponent as a root, evaluate it, and multiply the result by its original positive power to verify the reciprocal relationship.
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