Chapter 7.4, Problem 27MCQ

To determine

To State: The statement A number raised to a negative exponent is negative is always, sometimes or never true.

Answer to Problem 27MCQ

The required solution is that the statement is sometimes true.

Explanation of Solution

Given information:

The statement “A number raised to a negative exponent is negative”.

Calculation:

The given statement depends on the number and the exponent to be used.

For example,

  $\begin{array}{l}{2}^{-3}\\ =\frac{1}{2^3}\\ =\frac{1}{8}\end{array}$

It implies that $2^{-3}$ is positive.

  $\begin{array}{l}{\left(-2\right)}^{-3}\\ =\frac{1}{{\left(-2\right)}^3}\\ =\frac{1}{-8}\end{array}$

It implies ${\left(-2\right)}^{-3}$ is negative.

Therefore, The statement “A number raised to a negative exponent is negative” is sometimes true.