In Integrated Mathematics II students will begin the year by learning about fractional exponents. In this section they will learn that with fractional exponents the:
1. Numerator, or top of the fraction, is the power.
2. Denominator, or bottom of the fraction, is the root.
So 8⅔ is the cube root of 82. 82 is 64 and the cube root of 64 is 4 (because 4 x 4 x 4 = 64), so 8⅔ is 4.
Now it doesn’t matter which one you do first. I could have taken the cube root of 8 first, which is 2 (because 2 x 2 x 2 = 8), and then squared 2 (2 x 2) to get 4.
O.k. let’s try another one. How about 32⅖? Well I could first square 32, but that would be a huge number. Then I would have to try to take the square root of that. Instead what I think I should do is take the 5th root of 32 and then square it. O.k. so to do that we need to figure out a number that when multiplied by itself 5 times equals 32. Well that’s easy! 2 x 2 x 2 x 2 x 2 = 32 so the 5th root of 32 is 2.
O.k. so we know that the fifth root of 32 is 2, so now we have to square that number, when we do that we get 4 … again! I guess I like four.
O.k. one more … let’s try 27⅔ … I swear the answer won’t be four. O.k., so we could try to raise 27 to the 2nd power and then take the cube root of it, but again if we square 27 first we will get a HUGE number, then we have to try to find the cube root first. I think it’s better to just take the cube root of 27 first, which is 3 (because 3 x 3 x 3 = 27).
Now that we have that number we square it (3 x 3) to get 9. So our answer isn’t nine … see I also like nine.
Here are a few for you to try:
81¾
64⅔
64⅚
Give those a try …
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