Question

Express the number in a/b form where a and b are integers. (-.125)^2/3

Answer 1

\[\LARGE -\frac{1}{8}=-0.125\]

Answer 2

what

Answer 3

is that (-0.125)^2/3?

to change from decimal to fraction put a 1 under the decimal point and add as many 0 as significant figures after in the case -0.125 = -125/1000
this can be simplified
factors of 125 =5x5x5
factors of 1000 2x2x2x5x5x5
so divide by (cancel) 5x5x5 to get -1/8

now you have (-1/8)^2/3
from the rules of exponents same as (-1/8)^1/3 then ^2
8 can be written as 2^3 as above
(-1/2^3)^1/3 = (-1/2)^1 =-1/2
(-1/2)^2 = 1/4 negative times negative is positive

note that if you recognize the factors you can always do the powers first
(125/1000)^2/3
125 = 5^3
1000 = 10^3
(-5/10)^3 raised to the 2/3
=(-1/2)^(3)(2/3)
=(-1/2)^2
=1/4

my answer is 1/4