Q:

# How do you simplify fractions with exponents?

A:

Fractions with exponents are a natural extension of working with any set of mixed factors. Fortunately, there are some simple factoring steps to keep these terms as simple as possible.

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1. Simplify all terms with negative exponents

Rather than creating complex fractions in the factoring process, it is better to simplify any negative exponent first. Remember that x^-n = 1/x^n. Similarly, 1/x^-n = x^n. Find any term with a negative exponent and use these identities. Verify all exponents are positive when complete.

2. Factor all constants and combine like terms

Once constants are factored, determine how to simplify the constant terms by factoring into prime multiples. As an example, 48 = 2 x 2 x 2 x 2 x 3 = 2^4 x 3. Variables should be in the same order in the numerator as they are in the denominator. The terms can now be factored in an orderly fashion.

3. Cancel like terms in the numerator and denominator

Look for similar variables and constants that are both in the numerator and denominator. Cross off those that are the same. If the powers are not identical, cross out the lower power completely, but only cross out the exponent of the larger factor, noting the correct power after factoring. Once every term in the numerator cannot be factored by a term in the denominator, then the fraction is at its simplest form.

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