Question

I am trying to figure out how to evaluate 100^-3/2. I'm going by the example (64)^2/3=16. IN the example, 64^2/3 is changed into 64^1/3^2=4^2=16. But I don't get why out of all numbers it is changed into 4^2. I know 16 goes into 64 four times, but why is the answer 16 and what becomes of the 1/3? So how would this apply to 11^-3/2? Thanks for your help!

Answer 1

First, you'd have to adhere to the rules of priority.
The expression 64^2/3 is much clearer.
The 2 in the exponent requires us to square the base, and the 3 in the denominator represents (1/3) means we need to take the cube root of the base.
So whether you do ∛((64)²) or (∛64)³ will give the same answer, i.e. ∛(4096)=16 or (4)²=16. The 4 comes from the cube root of 64, or 64^1/3.

For 11^-3/2 it is the same procedure, by following the laws of exponents:
x^a+b = x^a × x^b
x^ab = (x^a)^b
x^-a = 1/x^a
x^1/a = ath root of x.

Therefore
11^-3/2
=1/11^3/2
=1/∛(11³)
=1/∛(1331)

Answer 2

11^-3/2
=1/11^3/2
=1/√(11³)
=1/√(1331)