Question

How do you do this. Please give a full answer and explain why.

Answer 1

Law of Exponent

`\displaystyle \large{ {a}^( - n) = \frac{1}{ {a}^(n) } }`

Compare the terms.

`\displaystyle \large{ {a}^( - n) = {( - 2)}^( - 3) }`

Therefore, a = -2 and n = 3. From the law of exponent above, we receive:

`\displaystyle \large{ {( - 2)}^( - 3) = \frac{1}{ {( - 2)}^( 3) } }`

Exponent Def. (For cubic)

`\displaystyle \large{ {a}^(3) = a * a * a }`

Factor (-2)^3 out.

`\displaystyle \large{ {( - 2)}^( - 3) = (1)/(( - 2) * ( - 2) * ( - 2))}`

(-2) • (-2) = 4 | Negative × Negative = Positive.

`\displaystyle \large{ {( - 2)}^( - 3) = (1)/(4 * ( - 2))}`

4 • (-2) = -8 | Negative Multiply Positive = Negative.

`\displaystyle \large{ {( - 2)}^( - 3) = (1)/( - 8)}`

If either denominator or numerator is in negative, it is the best to write in the middle or between numerator and denominators.

Hence,

`\displaystyle \large \boxed{ {( - 2)}^( - 3) = - (1)/( 8)}`

The answer is - 1 / 8