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What are some tips for solving expressions with negative exponents?

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Quick Answer

Moving a variable with a negative exponent to the opposite side of the fraction bar and changing the sign of the exponent to positive eliminates the negative exponents, allowing simplification of the fraction as normal. The negative exponent indicates the reciprocal of the term to the positive power.

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What are some tips for solving expressions with negative exponents?
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Full Answer

Exponents are a shorthand way of writing multiplication problems. Instead of writing "2x2x2," mathematicians use the expression "2^3." However, a negative exponent indicates the need for the opposite operation of multiplication, which is division. The value of the negative exponent indicates the number of times to divide by its base. As with numerical fractions, the method of solving division problems is to invert and multiply.

Because of the special mathematical properties of multiplication, there is often more than one way to simplify an exponential fraction. The answer remains the same if an individual multiplies the expressions on either side of the fraction bar before or after eliminating the negative exponents. When the term is a polynomial to a negative power, moving it before multiplying keeps the calculations simpler.

Simplifying algebraic fractions is similar to simplifying numeric fractions. It requires dividing both the numerator and denominator by the greatest common factor. In numeric fractions, "12/16" simplifies to "3/4." With algebraic fractions, "x^2/x^3" becomes "1/x." However, simplifying exponential fractions have more rules. These rules require students to remove any negative exponents from the fraction in their final answers.

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