Simplify 1/(10 square root of 10)

$\frac{1}{10 \sqrt{10}}$

Step 1

Multiply $\frac{1}{10 \sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{1}{10 \sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}$

Step 2

Combine and simplify the denominator.

Multiply $\frac{1}{10 \sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{\sqrt{10}}{10 \sqrt{10} \sqrt{10}}$

Move $\sqrt{10}$ .

$\frac{\sqrt{10}}{10 (\sqrt{10} \sqrt{10})}$

Raise $\sqrt{10}$ to the power of $1$ .

$\frac{\sqrt{10}}{10 ({\sqrt{10}}^{1} \sqrt{10})}$

Raise $\sqrt{10}$ to the power of $1$ .

$\frac{\sqrt{10}}{10 ({\sqrt{10}}^{1} {\sqrt{10}}^{1})}$

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

$\frac{\sqrt{10}}{10 {\sqrt{10}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{\sqrt{10}}{10 {\sqrt{10}}^{2}}$

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$\frac{\sqrt{10}}{10 {(10^{\frac{1}{2}})}^{2}}$

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

$\frac{\sqrt{10}}{10 \cdot 10^{\frac{1}{2} \cdot 2}}$

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

$\frac{\sqrt{10}}{10 \cdot 10^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{\sqrt{10}}{10 \cdot 10^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{\sqrt{10}}{10 \cdot 10^{1}}$

Evaluate the exponent.

$\frac{\sqrt{10}}{10 \cdot 10}$

Step 3

Multiply $10$ by $10$ .

$\frac{\sqrt{10}}{100}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{10}}{100}$

Decimal Form:

$0.03162277 \dots$