Calculus Examples

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

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

Tap for more steps...

Step 2.1

Move $x^{- \frac{1}{2}}$ .

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

Step 2.2

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

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

Step 2.3

Combine the numerators over the common denominator.

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

Step 2.4

Subtract $1$ from $- 1$ .

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

Step 2.5

Divide $- 2$ by $2$ .

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

Step 3

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

Tap for more steps...

Step 3.1

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

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

Step 3.2

Multiply $2$ by $2$ .

$\frac{1}{4} x^{- 1}$

Step 4

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

$\frac{1}{4} \cdot \frac{1}{x}$

Step 5

Multiply $\frac{1}{4}$ by $\frac{1}{x}$ .

$\frac{1}{4 x}$