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Positive fractional exponent simplification

This skill involves simplifying expressions with positive fractional exponents by rewriting them as roots. The denominator of the fraction indicates the root (e.g., cube root), and the expression under the exponent is factored to simplify further, removing fully cubed factors.

Learn positive fractional exponent simplification

Teaching Transcript

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Let's simplify this fractional exponent, 648 to the power of 1 third

Fractional exponents are the same as roots of the same order as the denominator, so this is the cube root of 648

We can factor 648 to a factorization of 3 twos and 4 threes

Since it's a cube root, we can remove cubed factors. A cubed 2 and a cubed 3 can be removed, leaving an answer of 6 times the cube root of 3

Skill Practice

Positive fractional exponent simplification

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