Chapter 13.2, Problem 11AR

To determine

To simplify $2^3\cdot 2^2\cdot 2^{-4}$.

Answer to Problem 11AR

The required solution is $2^3\cdot 2^2\cdot 2^{-4}=2$ .

Explanation of Solution

Given information: The number is $2^3\cdot 2^2\cdot 2^{-4}$ .

Calculation: The required solution is obtained as,

When there is a negative exponent, just put the whole thing under 1 and get rid of the negative.

  $\begin{array}{l}{2}^3\cdot 2^2\cdot 2^{-4}\\ =8\cdot 4\cdot \frac{1}{2^4}\\ =32\cdot \frac{1}{16}\\ =2\end{array}$

Hence, the required solution is $2^3\cdot 2^2\cdot 2^{-4}=2$ .