Question

Simplify the expression ${81}^{\sqrt{2}}÷3^{\sqrt{2}}$.

Short answer

The simplified value of expression is ${27}^{\sqrt{2}}$.

Step-by-step solution

Step 1. Write down the given expression.

The given expression is ${81}^{\sqrt{2}}÷3^{\sqrt{2}}$.

Step 2. Simplify the expression.

The given expression ${81}^{\sqrt{2}}÷3^{\sqrt{2}}$is simplified as:

$\begin{array}{l}{81}^{\sqrt{2}}÷3^{\sqrt{2}}=\frac{{\left(81\right)}^{\sqrt{2}}}{{\left(3\right)}^{\sqrt{2}}}\\ =\frac{{\left(3^4\right)}^{\sqrt{2}}}{{\left(3\right)}^{\sqrt{2}}}\\ =\frac{{\left(3\right)}^{4\sqrt{2}}}{{\left(3\right)}^{\sqrt{2}}}\\ =3^{3\sqrt{2}}\\ ={27}^{\sqrt{2}}\end{array}$

Step 3. Conclusion.

The simplified value of expression is ${27}^{\sqrt{2}}$.