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Fractional base raised to fractional exponent

Fractional base raised to a negative fractional exponent

This skill teaches how to calculate a fractional base raised to a negative fractional exponent. It involves converting the exponent to a positive by taking the reciprocal of the base and interpreting the fractional exponent as a root, simplifying to find the final value.

Learn fractional base raised to fractional exponent

Teaching Transcript

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What is 4 over 9, all raised to the power of negative one half?

First, negative exponents mean a reciprocal, so this is the same as 9 over 4, all raised to the power of positive one half

Fractional exponents are roots of that index, so this is a square root

The square root of 9 over 4 is the same as root 9, over root 4

We can solve both of those, so we have a final answer of 3 over 2.

Skill Practice

Fractional base raised to a negative fractional exponent

Test your understanding of fractional base raised to fractional exponent by practicing it! Work through the below exercises to use it in practice.