Basic Math Examples

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

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Simplify the denominator.

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Step 2.1

Rewrite ${(- 1)}^{\frac{1}{2}}$ as $\sqrt{{(- 1)}^{1}}$ .

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

Step 2.2

Evaluate the exponent.

$\frac{1}{\sqrt{- 1}}$

Step 2.3

Rewrite $\sqrt{- 1}$ as $i$ .

$\frac{1}{i}$

Step 3

Multiply the numerator and denominator of $\frac{1}{i}$ by the conjugate of $i$ to make the denominator real.

$\frac{1}{i} \cdot \frac{i}{i}$

Step 4

Multiply.

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Step 4.1

Combine.

$\frac{1 i}{i i}$

Step 4.2

Multiply $i$ by $1$ .

$\frac{i}{i i}$

Step 4.3

Simplify the denominator.

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Step 4.3.1

Raise $i$ to the power of $1$ .

$\frac{i}{i^{1} i}$

Step 4.3.2

Raise $i$ to the power of $1$ .

$\frac{i}{i^{1} i^{1}}$

Step 4.3.3

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

$\frac{i}{i^{1 + 1}}$

Step 4.3.4

Add $1$ and $1$ .

$\frac{i}{i^{2}}$

Step 4.3.5

Rewrite $i^{2}$ as $- 1$ .

$\frac{i}{- 1}$

Step 5

Move the negative one from the denominator of $\frac{i}{- 1}$ .

$- 1 \cdot i$

Step 6

Rewrite $- 1 \cdot i$ as $- i$ .

$- i$