Expert: Sherry Wallin - 11/24/2008

Question
simplify:    a^-6 b^10 divided by 5c^7 d^-2

Answer
Hi Karen~
    I tell my students to think of the numerator as the attic and the denominator as the basement and when an exponent is negative move the factor with the exponent to wherever it is not originally and change the sign on the exponent. So for example, one of the factors you have is a^-6, and -6 is negative so take the a^-6 out of the attic and send it to the basement and make the -6 a  6 so you now have a^-6 = 1/a^6.
For the complete solution:

a^-6 b^10 divided by 5c^7 d^-2 = a^-6*b^10/5c^7*d^-2. You already know that a^-6 is 1/a^6 and the only other negative exponent is the -2 in d^-2 in the basement so move the d^-2 to the attic and change it's sign so you now have 1/d^-2 = d^2. Collect our new found information and notice we didn't have to do anything with b^10/5c^7 since there aren't any negative exponents in these factors.

Result: b^10*d^2/5a^6*c^7. I moved the 5 in front of the variables in the basement since this is common in simplifying to put coefficients in front of the expression.

I hope this is clear for you, and if not, please feel free to ask for additional help.

Math Prof