Basic Math Examples

$r^{- \frac{1}{2}} \cdot r^{- \frac{1}{2}} \cdot r^{\frac{1}{2}}$

Step 1

Multiply $r^{- \frac{1}{2}}$ by $r^{- \frac{1}{2}}$ by adding the exponents.

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Step 1.1

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

$r^{- \frac{1}{2} - \frac{1}{2}} \cdot r^{\frac{1}{2}}$

Step 1.2

Combine the numerators over the common denominator.

$r^{\frac{- 1 - 1}{2}} \cdot r^{\frac{1}{2}}$

Step 1.3

Subtract $1$ from $- 1$ .

$r^{\frac{- 2}{2}} \cdot r^{\frac{1}{2}}$

Step 1.4

Divide $- 2$ by $2$ .

$r^{- 1} \cdot r^{\frac{1}{2}}$

Step 2

Multiply $r^{- 1}$ by $r^{\frac{1}{2}}$ by adding the exponents.

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Step 2.1

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

$r^{- 1 + \frac{1}{2}}$

Step 2.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$r^{- 1 \cdot \frac{2}{2} + \frac{1}{2}}$

Step 2.3

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

$r^{\frac{- 1 \cdot 2}{2} + \frac{1}{2}}$

Step 2.4

Combine the numerators over the common denominator.

$r^{\frac{- 1 \cdot 2 + 1}{2}}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 1$ by $2$ .

$r^{\frac{- 2 + 1}{2}}$

Step 2.5.2

Add $- 2$ and $1$ .

$r^{\frac{- 1}{2}}$

Step 2.6

Move the negative in front of the fraction.

$r^{- \frac{1}{2}}$

Step 3

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

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