SOLUTION: write an equivalent expression using radical notation 16 3/4

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Question 613119: write an equivalent expression using radical notation

16 3/4
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
In general,
a%5E%28p%2Fq%29+=+root%28q%2C+a%5Ep%29 (or %28root%28q%2C+a%29%29%5Ep) Either one can be used. They are equivalent. In a particular problem, use whichever one looks easier.

So
16%5E%283%2F4%29+=+root%284%2C+16%5E3%29 or %28root%284%2C+16%29%29%5E3

These radical expressions can be simplified. Since 16+=+2%5E4 the 4th root of 16 is easy to find. So I'm going to use the second, "cube of the root" expression instead of the first, "root of the cube" expression:
16%5E%283%2F4%29+=+%28root%284%2C+16%29%29%5E3+=+2%5E3+=+8

If I had used the "root of the cube", root%284%2C+16%5E3%29, instead, I would have had to cube 16 (yuck!) first and then find the 4th root of the whatever 16 cubed is (double yuck!). But I would still end up with 8!