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Chapter 0: Problem 7

Evaluate the expressions. $$ (-2)^{-3} $$

Short Answer

Expert verified
The expression \((-2)^{-3}\) can be rewritten as \(\frac{1}{(-2)^{3}}\) using the rule for negative exponents. Evaluating this expression, we get \(\frac{1}{-8}\).

Step by step solution

01

Recall the rule for negative exponents

Recall that for any non-zero number \(a\) and integer \(n\), a number raised to a negative exponent is equal to the reciprocal of the number raised to the positive exponent. In other words, we have: \(a^{-n} = \frac{1}{a^{n}}\) This rule will help us to rewrite the given expression in a more familiar form.
02

Rewrite the expression using the rule for negative exponents

Applying the rule of negative exponents, we can rewrite the given expression as: \((-2)^{-3} = \frac{1}{(-2)^{3}}\)
03

Evaluate the expression

Now that we have a positive exponent in our expression, we can proceed with the calculations: \(\frac{1}{(-2)^{3}} = \frac{1}{-2 \cdot -2 \cdot -2} = \frac{1}{-8}\) The expression \((-2)^{-3}\) evaluates to \(\frac{1}{-8}\).

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