Chapter 5 - Section 5.2 - More Work with Exponents and Scientific Notation - Exercise Set: 100

No

Work Step by Step

We know that $a^{-n}=\frac{1}{a^{n}}$ for some nonzero real number a and some positive integer n. Therefore, we know that $a^{-2}=\frac{1}{a^{2}}$. We know that the square of any real number will be positive, which would make the denominator of $\frac{1}{a^{2}}$ positive. Since, both the numerator and denominator are positive, we know that $\frac{1}{a^{2}}$ will also be positive. So, there is no number a such that $a^{-2}$ will be a negative number.

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