Evaluate 1/( square root of e)

$\frac{1}{\sqrt{e}}$

Step 1

Multiply $\frac{1}{\sqrt{e}}$ by $\frac{\sqrt{e}}{\sqrt{e}}$ .

$\frac{1}{\sqrt{e}} \cdot \frac{\sqrt{e}}{\sqrt{e}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{e}}$ by $\frac{\sqrt{e}}{\sqrt{e}}$ .

$\frac{\sqrt{e}}{\sqrt{e} \sqrt{e}}$

Raise $\sqrt{e}$ to the power of $1$ .

$\frac{\sqrt{e}}{{\sqrt{e}}^{1} \sqrt{e}}$

Raise $\sqrt{e}$ to the power of $1$ .

$\frac{\sqrt{e}}{{\sqrt{e}}^{1} {\sqrt{e}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sqrt{e}}{{\sqrt{e}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{e}}{{\sqrt{e}}^{2}}$

Rewrite ${\sqrt{e}}^{2}$ as $e$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{e}$ as $e^{\frac{1}{2}}$ .

$\frac{\sqrt{e}}{{(e^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{\sqrt{e}}{e^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{\sqrt{e}}{e^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{e}}{e^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{e}}{e^{1}}$

Simplify.

$\frac{\sqrt{e}}{e}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{e}}{e}$

Decimal Form:

$0.60653065 \dots$