Chapter 7.2, Problem 33PPE

To determine

To complete: The equation $2^{\_}\cdot 2^{\frac{1}{2}}=2^1$

Answer to Problem 33PPE

The required answer is: $2^{\frac{1}{2}}\cdot 2^{\frac{1}{2}}=2^1$ .

Explanation of Solution

Given information:

The given equation: $2^{\_}\cdot 2^{\frac{1}{2}}=2^1$

Calculation:

  $\begin{array}{l}\Rightarrow 2^{\_}\cdot 2^{\frac{1}{2}}=2^1\\ \Rightarrow 2^{\frac{1}{2}}\cdot 2^{\frac{1}{2}}=2^1\\ \Rightarrow 2^{\frac{1}{2}+\frac{1}{2}}=2^1\end{array}$

(Add the exponents that have the same base)

  $\Rightarrow 2^1=2^1$

(Simplify)

Therefore, $2^{\frac{1}{2}}\cdot 2^{\frac{1}{2}}=2^1$ .