After talking with you here are two different options I think you are trying to ask:
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If you are talking about: [tex](\frac{-12}{3}) ^{3}[/tex]
Answer: -62
Explanation:
PEMDAS tells us we need to do the exponent first:
-12³ = (-12)³ = -1728
The parentheses are important so you cube the negative sign as well!
3³ = 27
-1728 / 27 = -62
[tex](\frac{-12}{3}) ^{3}[/tex] simplified is -62
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If you are talking about (-1[tex]\frac{2}{3}[/tex])³
Answer: -[tex]\frac{125}{27}[/tex]
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 [tex]-\frac{5}{3}[/tex]
To cube it we must do:
([tex]-\frac{5}{3}[/tex])([tex]-\frac{5}{3}[/tex])([tex]-\frac{5}{3}[/tex])
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[tex]\frac{2}{3}[/tex])³ simplifed is -[tex]\frac{125}{27}[/tex]
