Algebra Examples

${(\frac{1}{\sqrt{2}})}^{0}$

Step 1

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

${(\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}})}^{0}$

Step 2

Combine and simplify the denominator.

Tap for more steps...

Step 2.1

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

${(\frac{\sqrt{2}}{\sqrt{2} \sqrt{2}})}^{0}$

Step 2.2

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

${(\frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}})}^{0}$

Step 2.3

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

${(\frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}})}^{0}$

Step 2.4

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

${(\frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}})}^{0}$

Step 2.5

Add $1$ and $1$ .

${(\frac{\sqrt{2}}{{\sqrt{2}}^{2}})}^{0}$

Step 2.6

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

Tap for more steps...

Step 2.6.1

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

${(\frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}})}^{0}$

Step 2.6.2

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

${(\frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}})}^{0}$

Step 2.6.3

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

${(\frac{\sqrt{2}}{2^{\frac{2}{2}}})}^{0}$

Step 2.6.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.6.4.1

Cancel the common factor.

${(\frac{\sqrt{2}}{2^{\frac{2}{2}}})}^{0}$

Step 2.6.4.2

Rewrite the expression.

${(\frac{\sqrt{2}}{2^{1}})}^{0}$

Step 2.6.5

Evaluate the exponent.

${(\frac{\sqrt{2}}{2})}^{0}$

Step 3

Simplify the expression.

Tap for more steps...

Step 3.1

Apply the product rule to $\frac{\sqrt{2}}{2}$ .

$\frac{{\sqrt{2}}^{0}}{2^{0}}$

Step 3.2

Anything raised to $0$ is $1$ .

$\frac{1}{2^{0}}$

Step 3.3

Anything raised to $0$ is $1$ .

$\frac{1}{1}$

Step 3.4

Divide $1$ by $1$ .

$1$