Chapter 7.2, Problem 48PPE

To determine

To Simplify: The expression $2^n\cdot 2^{n+2}\cdot 2$ .

Answer to Problem 48PPE

The required answer is $2^{2n+3}$ .

Explanation of Solution

Given information:

The expression $2^n\cdot 2^{n+2}\cdot 2$

Calculation:

  $\begin{array}{l}{2}^n\cdot 2^{n+2}\cdot 2\\ =2^n\cdot 2^{n+2}\cdot 2^1\end{array}$

(Write 2 as $2^1$ )

  $=2^{n+n+2+1}$

(Add the exponents that have the same base)

  $=2^{2n+3}$

(Simplify the exponent)