Calculus Examples

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

Step 1

Move $x^{\frac{1}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

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

Step 2

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $2$ by $2$ .

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

Step 2.5.2

Subtract $1$ from $4$ .

$x^{\frac{3}{2}}$