Calculus Examples

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

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

Step 1

Move

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

$x^{\frac{1}{2}}$ to the numerator using the negative exponent rule

\frac{1}{b^{n}} = b^{- n}

$\frac{1}{b^{n}} = b^{- n}$ .

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

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

Step 2

Multiply

x^{2}

$x^{2}$ by

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

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

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Step 2.1

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

Step 2.2

To write

2

$2$ as a fraction with a common denominator, multiply by

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 2.3

Combine

2

$2$ and

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply

2

$2$ by

2

$2$ .

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

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

Step 2.5.2

Subtract

1

$1$ from

4

$4$ .

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

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

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

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

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

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

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

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

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