Chapter 13.2, Problem 17AR

To determine

To simplify. Use only positive exponents $a\cdot a^{-1}$.

Answer to Problem 17AR

The required solution is $a\cdot a^{-1}=1$ .

Explanation of Solution

Given information: The number is $a\cdot a^{-1}$ .

Calculation: The required solution is obtained as,

When you multiply two exponents with the same number, you add them. And there is no exponent, there is an invisible power 1 in front. So $-1+1=0$ , and anything to the power 0 is 1.

  $\begin{array}{l}a\cdot a^{-1}\\ =a\cdot \frac{1}{a^1}\\ =1\end{array}$

Hence, the required solution is $a\cdot a^{-1}=1$ .