Calculus Examples

t^{2} (t^{\frac{1}{2}})

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

Step 1

Use the power rule

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

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

t^{2 + \frac{1}{2}}

$t^{2 + \frac{1}{2}}$

Step 2

To write

2

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

\frac{2}{2}

$\frac{2}{2}$ .

t^{2 \cdot \frac{2}{2} + \frac{1}{2}}

$t^{2 \cdot \frac{2}{2} + \frac{1}{2}}$

Step 3

Combine

2

$2$ and

\frac{2}{2}

$\frac{2}{2}$ .

t^{\frac{2 \cdot 2}{2} + \frac{1}{2}}

$t^{\frac{2 \cdot 2}{2} + \frac{1}{2}}$

Step 4

Combine the numerators over the common denominator.

t^{\frac{2 \cdot 2 + 1}{2}}

$t^{\frac{2 \cdot 2 + 1}{2}}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply

2

$2$ by

2

$2$ .

t^{\frac{4 + 1}{2}}

$t^{\frac{4 + 1}{2}}$

Step 5.2

Add

4

$4$ and

1

$1$ .

t^{\frac{5}{2}}

$t^{\frac{5}{2}}$

t^{\frac{5}{2}}

$t^{\frac{5}{2}}$