Evaluate an expression with negative exponents

Question
((1/2)^-3) -1 : need a step-by-step process on how we obtain the answer, 7.

Answer
STEP 1:    To simplify the given expression:
simplify the expression ((1/2)^-3)-1
we should first simplify the term,
simplify the term (1/2)^-3
and then subtract 1 from the obtained answer. We note that this term has negative exponent "–3".

The negative exponent rule states that any nonzero number raised to a negative power equals its reciprocal raised to the positive power. For instance, x-3 can be rewritten as:
1/x^3

Now, let us rewrite the term,
(1/2)^(-3)

using the negative exponent rule.

We write the reciprocal of 1/2 first, and then raise it to the positive power 3.

simplified ((1/2)^-3)


STEP 2:   Now, we are left with the expression 23 –1. Let us recall the exponential notation to simplify this expression.

For any natural number n means:
n factors of b

So, here it means that 2 is to be multiplied 3 times. We then subtract 1 from 23.
the answer is 7

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