Evaluate 1/( square root of 14)

$\frac{1}{\sqrt{14}}$

Step 1

Multiply $\frac{1}{\sqrt{14}}$ by $\frac{\sqrt{14}}{\sqrt{14}}$ .

$\frac{1}{\sqrt{14}} \cdot \frac{\sqrt{14}}{\sqrt{14}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{1}{\sqrt{14}}$ by $\frac{\sqrt{14}}{\sqrt{14}}$ .

$\frac{\sqrt{14}}{\sqrt{14} \sqrt{14}}$

Raise $\sqrt{14}$ to the power of $1$ .

$\frac{\sqrt{14}}{{\sqrt{14}}^{1} \sqrt{14}}$

Raise $\sqrt{14}$ to the power of $1$ .

$\frac{\sqrt{14}}{{\sqrt{14}}^{1} {\sqrt{14}}^{1}}$

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

$\frac{\sqrt{14}}{{\sqrt{14}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{14}}{{\sqrt{14}}^{2}}$

Rewrite ${\sqrt{14}}^{2}$ as $14$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{14}$ as $14^{\frac{1}{2}}$ .

$\frac{\sqrt{14}}{{(14^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt{14}}{14^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{14}}{14^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{14}}{14^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{14}}{14^{1}}$

Evaluate the exponent.

$\frac{\sqrt{14}}{14}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{14}}{14}$

Decimal Form:

$0.26726124 \dots$