Question

Simplify the expression $7^{\sqrt{2}}·7^{3\sqrt{2}}$.

Short answer

The simplified value of expression is ${2401}^{\sqrt{2}}$.

Step-by-step solution

Step 1. Write down the given expression.

The given expression is $7^{\sqrt{2}}·7^{3\sqrt{2}}$.

Step 2. Simplify the expression.

The given expression $7^{\sqrt{2}}·7^{3\sqrt{2}}$is simplified as:

$\begin{array}{l}{7}^{\sqrt{2}}\cdot 7^{3\sqrt{2}}={\left(7\right)}^{\sqrt{2}}\cdot {\left(7\right)}^{3\sqrt{2}}\\ ={\left(7\right)}^{4\sqrt{2}}\\ ={\left(7^4\right)}^{\sqrt{2}}\\ ={2401}^{\sqrt{2}}\end{array}$

Step 3. Conclusion.

The simplified value of expression is ${2401}^{\sqrt{2}}$.