Question 224209: express ^3sqrt(8a^3 y^2) using rational exponents
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! 
First you need to sort this problem into TWO separate cube roots, and put all the perfect cube factors in the first cube root, and all the leftover factors in the second one. Cubes are numbers like 8, 27, 64, and 125. You really need to know these "special numbers" before you ever start a cube root problem.
Now, 
You can do the first cube root, so DO IT! You can't do the second cube root, so leave it alone:
For an additional explanation of Cube Roots, see my own website by doing a "Bing" search for my last name "Rapalje". Look for my website "Rapalje Homepage" near the top of the search list. On my webpage, look for "Basic, Intermediate and College Algebra: One Step at a Time." Select "Intermediate Algebra" and look in "Chapter 3," "Section 3.01 Radicals." If this seems hard for you to understand, then go back to "Basic Algebra" and look in "Chapter 5" for "Section 5.02 Cube Roots and More". This is my own non-traditional explanation that my own students ALL found easier to understand than the one given in traditional textbooks. See also the corresponding section in my "MATH IN LIVING COLOR" pages in which I solved a lot of these types of problems in COLOR!! I also have a video that was made in one of my classes a few years ago teaching this lesson. You can see this video FREE on my website. From my Homepage, look for the link "Rapalje Videos in Living Color," choose "Basic Algebra," and look for the topic "Radicals (Square Roots)." In Intermediate Algebra, the video is called "Radicals and Fractional Exponents."
R^2
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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