Alden G. answered • 08/16/20
UMass Lowell Electrical Engineering Grad | 3 Years Industry Experience
A number like 27-(2/3) can look weird at first before observing how you can work with the exponent. Let's look at some simple ways to see past the puzzle of this problem:
1) We have a negative exponent here. That means this number is going to be 1 / (27)(2/3) if we rearrange it in this form.
2) For exponents in fraction form, we identify that the denominator is the nth root of the number being raised to an exponent, and the numerator is that root of the number being raised to an nth power.
In that case:
27(2/3) is really just a exponential way of taking the cubed root of 27 and raising that value to the second power.
We know the cubed root of 27 is 3, and 3 to the second power is 9.
We also need to remember our fractional exponent was originally negative, so just take that value we just found, and flip the numerator and denominator of it. 9 is also (9/1) in fraction form, so we're left with (1/9).
Our answer is (1/9) in that case. Since both of these values in our fraction are integers, we are all done.
Hope this helps!
