After talking with you here are two different options I think you are trying to ask:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
If you are talking about: ![(\frac{-12}{3}) ^{3}](https://tex.z-dn.net/?f=%28%5Cfrac%7B-12%7D%7B3%7D%29%20%5E%7B3%7D)
Answer: -62
Explanation:
PEMDAS tells us we need to do the exponent first:
-12³ = (-12)³ = -1728
<em>The parentheses are important so you cube the negative sign as well!</em>
3³ = 27
-1728 / 27 = -62
simplified is -62
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
If you are talking about (-1
)³
Answer: -![\frac{125}{27}](https://tex.z-dn.net/?f=%5Cfrac%7B125%7D%7B27%7D)
Explanation:
First, let us turn -1 and two thirds into a mixed number:
Ignoring the negative for now, we can 1 times 3 is 3. 3 plus 2 is 5. 5/3 is 5/3. Adding in the negative we get ![-\frac{5}{3}](https://tex.z-dn.net/?f=-%5Cfrac%7B5%7D%7B3%7D)
To cube it we must do:
(
)(
)(
)
3 times 3 (9) times 3 is 27
5 times 5 (25) times 5 is 125
So we have 125/27
For the negative, we have three - - -
Two cancel each other out, and we are left with one (-) so our answer is negative
(-1
)³ simplifed is -![\frac{125}{27}](https://tex.z-dn.net/?f=%5Cfrac%7B125%7D%7B27%7D)