Expanding a Rational Expression

Dear Professor Cram:

I am taking a distance learning college algebra course, so I am left on my own to some extent to learn the material. I'm just beginning to work problems like: (5x²/6y²)³

The book I'm using doesn't give me an example of this type of problem. Where do I start?

Marilyn D., Lancaster, CA

Thank you for using College-Cram.com and for your Algebra question.

The best way to expand this rational expression is to recall that raising anything to the power of three means to multiply it by itself three times. Thus, your expression becomes:

  • (5x²/6y²)(5x²/6y²)(5x²/6y²)

Since these are fractions, let's reorganize it so we have the product of the numerators (numbers on top) divided by the product of the denominators (numbers on the bottom):

  • ((5x²)(5x²)(5x²)) / ((6y²)(6y²)(6y²))

To multiply these out, multiply the coefficients and add the exponents:

  • 125x6/216y6

This result is equal to your original rational expression, only expanded.

I hope this helps. Let us know if you need anything else.

Good studying,

Professor Cram