Law of Exponent
[tex] \displaystyle \large{ {a}^{ - n} = \frac{1}{ {a}^{n} } }[/tex]
Compare the terms.
[tex] \displaystyle \large{ {a}^{ - n} = {( - 2)}^{ - 3} }[/tex]
Therefore, a = -2 and n = 3. From the law of exponent above, we receive:
[tex] \displaystyle \large{ {( - 2)}^{ - 3} = \frac{1}{ {( - 2)}^{ 3} } }[/tex]
Exponent Def. (For cubic)
[tex] \displaystyle \large{ {a}^{3} = a \times a \times a }[/tex]
Factor (-2)^3 out.
[tex] \displaystyle \large{ {( - 2)}^{ - 3} = \frac{1}{( - 2) \times ( - 2) \times ( - 2)}}[/tex]
(-2) • (-2) = 4 | Negative × Negative = Positive.
[tex] \displaystyle \large{ {( - 2)}^{ - 3} = \frac{1}{4 \times ( - 2)}}[/tex]
4 • (-2) = -8 | Negative Multiply Positive = Negative.
[tex] \displaystyle \large{ {( - 2)}^{ - 3} = \frac{1}{ - 8}}[/tex]
If either denominator or numerator is in negative, it is the best to write in the middle or between numerator and denominators.
Hence,
[tex] \displaystyle \large \boxed{ {( - 2)}^{ - 3} = - \frac{1}{ 8}}[/tex]
The answer is - 1 / 8
