How to Rewrite an Expression With Positive Exponents

By Kristy Wedel

If you have an expression with negative exponents, you can rewrite it with positive exponents by moving around the terms. A negative exponent indicates the number of times to divide by the term. This is the opposite of a positive exponent, which indicates the number of times to multiply the term. To rewrite the expression with positive exponents, you must move the terms with negative exponents from the numerator to the denominator or from the denominator to the numerator, depending on where the terms are located.

Move any negative exponents from the numerator (the top of the fraction) to the denominator (the bottom of the fraction). Doing so eliminates the negative in the exponent. For example, if given the expression [(x^(-2))(xy^3)]/(4_x^(-4)), first look at [(x^(-2))(xy^3)]. In this expression (x^(-2)) has a negative exponent but (xy^3) does not. Move (x^(-2)) to the denominator and it will become (x^(2)). Leave (xy^3) in the numerator. So now the expression is (xy^3)/ [(x^(2))(4_x^(-4))].

Move any negative exponents from the denominator (the bottom of the fraction) to the numerator (the top of the fraction). In the example (xy^3)/ [(x^(2))(4*x^(-4))], the term (x^(-4)) in the denominator has a negative exponent. Note that although 4 is being multiplied by x^(-4), it is not being raised to a negative power and it should not be moved. Move x^(-4) to the numerator to get [x^(4) (xy^3)]/ [(x^(2))(4)].

Organize and simplify the expression. [x^(4) (xy^3)]/ [(x^(2))(4)] can be simplified to ((xy)^3)/4.

About the Author

I have a bachelor’s degree in mathematics from OSU and have written numerous articles on mathematics for eHow. I also have over 5 years experience in computer software/hardware troubleshooting. I have written many software troubleshooting documents as well as user guides for software packages such as MS Office and popular media software.