# 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:

we should first simplify the term,

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:

Now, let us rewrite the term,

using the negative exponent rule.

We write the reciprocal of

^{1}/

_{2} first, and then raise it to the positive power 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:

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

^{3}.