SOLUTION: The examples in the book: a. 27 to the power of 2/3 = (27 to the power of 1/3)squared = (3)squared = 9 {3x3 = 9 yes but why is 9 the answer to 27 to the power of 2/3? b.

Algebra ->  Square-cubic-other-roots -> SOLUTION: The examples in the book: a. 27 to the power of 2/3 = (27 to the power of 1/3)squared = (3)squared = 9 {3x3 = 9 yes but why is 9 the answer to 27 to the power of 2/3? b.      Log On


   

Question 28572: The examples in the book:
a. 27 to the power of 2/3 = (27 to the power of 1/3)squared = (3)squared = 9 {3x3 = 9 yes but why is 9 the answer to 27 to the power of 2/3?


b. 16 to the power of 3/4 = (16 to the power of 1/4)cubed = 2 cubed = 8 {I do not see the relationship between 2 cubed or 8 and (16 to the power of 1/4) cubed.
The examples continue in this way and I am stuck. I cannot do any more homework.
Answer by askmemath(368) About Me  (Show Source):
You can put this solution on YOUR website!
Let me begin by defining Square of a Number
The square of a number is that number multiplied by itself
i.eX%5E2+=+X%2AX
Similarly Cube of a number is that number multiplied by itself 3 times
i.e. If X is the number then X%5E3+=+X%2AX%2AX
Now 27 = 3*3*3 thus we can say that 3 is the Cube Root of 27
Any number when raised to the power 1/n and then again raised to power n = the number itself
i.e. 1%2Fn+%2A+n+=+1
but if it was say 2/n then it becomes 2%2Fn+%2A+n+=+2
which now becomes the square of the number
thus %2827%29%5E%282%2F3%29=+%283%5E3%29%5E%282%2F3%29+=3%5E2+=+9
Now can you do for the rest of the numbers?