Algebra Examples

$\frac{\sqrt{2}}{\frac{2}{\frac{\sqrt{2}}{2}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{2} \frac{\frac{\sqrt{2}}{2}}{2}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{2} (\frac{\sqrt{2}}{2} \cdot \frac{1}{2})$

Step 3

Multiply $\frac{\sqrt{2}}{2} \cdot \frac{1}{2}$ .

Tap for more steps...

Step 3.1

Multiply $\frac{\sqrt{2}}{2}$ by $\frac{1}{2}$ .

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

Step 3.2

Multiply $2$ by $2$ .

$\sqrt{2} \frac{\sqrt{2}}{4}$

Step 4

Multiply $\sqrt{2} \frac{\sqrt{2}}{4}$ .

Tap for more steps...

Step 4.1

Combine $\sqrt{2}$ and $\frac{\sqrt{2}}{4}$ .

$\frac{\sqrt{2} \sqrt{2}}{4}$

Step 4.2

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{{\sqrt{2}}^{1} \sqrt{2}}{4}$

Step 4.3

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{{\sqrt{2}}^{1} {\sqrt{2}}^{1}}{4}$

Step 4.4

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

$\frac{{\sqrt{2}}^{1 + 1}}{4}$

Step 4.5

Add $1$ and $1$ .

$\frac{{\sqrt{2}}^{2}}{4}$

Step 5

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

Tap for more steps...

Step 5.1

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

$\frac{{(2^{\frac{1}{2}})}^{2}}{4}$

Step 5.2

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

$\frac{2^{\frac{1}{2} \cdot 2}}{4}$

Step 5.3

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

$\frac{2^{\frac{2}{2}}}{4}$

Step 5.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 5.4.1

Cancel the common factor.

$\frac{2^{\frac{2}{2}}}{4}$

Step 5.4.2

Rewrite the expression.

$\frac{2^{1}}{4}$

Step 5.5

Evaluate the exponent.

$\frac{2}{4}$

Step 6

Cancel the common factor of $2$ and $4$ .

Tap for more steps...

Step 6.1

Factor $2$ out of $2$ .

$\frac{2 (1)}{4}$

Step 6.2

Cancel the common factors.

Tap for more steps...

Step 6.2.1

Factor $2$ out of $4$ .

$\frac{2 \cdot 1}{2 \cdot 2}$

Step 6.2.2

Cancel the common factor.

$\frac{2 \cdot 1}{2 \cdot 2}$

Step 6.2.3

Rewrite the expression.

$\frac{1}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$