Question

Simplify the expression $2^{\sqrt{7}}·2^{\sqrt{7}}$.

Short answer

The simplified value of expression is $2^{2\sqrt{7}}$.

Step-by-step solution

Step 1. Write down the given expression.

The given expression is $2^{\sqrt{7}}·2^{\sqrt{7}}$.

Step 2. Simplify the expression.

The given expression $2^{\sqrt{7}}·2^{\sqrt{7}}$is simplified as:

$\begin{array}{l}{2}^{\sqrt{7}}\cdot 2^{\sqrt{7}}={\left(2\right)}^{\sqrt{7}}\cdot {\left(2\right)}^{\sqrt{7}}\\ ={\left(2\right)}^{\sqrt{7}+\sqrt{7}}\\ ={\left(2\right)}^{2\sqrt{7}}\\ =2^{2\sqrt{7}}\end{array}$

Step 3. Conclusion.

The simplified value of expression is $2^{2\sqrt{7}}$.