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Negative fractional exponent simplification

This math skill involves simplifying expressions with negative fractional exponents. First, a negative exponent is expressed as the reciprocal of the base raised to the positive of that exponent. Then, the fractional exponent is converted to a root, and any radicals are simplified if possible.

Learn negative fractional exponent simplification

Teaching Transcript

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Let's simplify this negative fractional exponent, 200 to the power of negative one half

A negative exponent means 1 over the positive of that exponent, so we can rewrite this as 1 over 200 to the power of one half

A fractional exponent is the same as a root of the same order as the denominator, so we can rewrite as 1 over the square root of 200

Now let's factor the radical. 200 is 2 times 2 times 2 times 5 times 5

We have a squared 2 and a squared 5 that we can remove, so our final answer becomes 1 over 10 root 2

Skill Practice

Negative fractional exponent simplification

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