Calculus Examples

$F (3) = \frac{9}{4} \cdot {(3)}^{4}$

Step 1

Simplify.

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Step 1.1

Raise $3$ to the power of $4$ .

$F (3) = \frac{9}{4} \cdot 81$

Step 1.2

Multiply $\frac{9}{4} \cdot 81$ .

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Step 1.2.1

Combine $\frac{9}{4}$ and $81$ .

$F (3) = \frac{9 \cdot 81}{4}$

Step 1.2.2

Multiply $9$ by $81$ .

$F (3) = \frac{729}{4}$

Step 2

Divide each term in $F (3) = \frac{729}{4}$ by $3$ and simplify.

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Step 2.1

Divide each term in $F (3) = \frac{729}{4}$ by $3$ .

$\frac{F (3)}{3} = \frac{\frac{729}{4}}{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{F \cdot 3}{3} = \frac{\frac{729}{4}}{3}$

Step 2.2.1.2

Divide $F$ by $1$ .

$F = \frac{\frac{729}{4}}{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$F = \frac{729}{4} \cdot \frac{1}{3}$

Step 2.3.2

Cancel the common factor of $3$ .

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Step 2.3.2.1

Factor $3$ out of $729$ .

$F = \frac{3 (243)}{4} \cdot \frac{1}{3}$

Step 2.3.2.2

Cancel the common factor.

$F = \frac{3 \cdot 243}{4} \cdot \frac{1}{3}$

Step 2.3.2.3

Rewrite the expression.

$F = \frac{243}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$F = \frac{243}{4}$

Decimal Form:

$F = 60.75$

Mixed Number Form:

$F = 60 \frac{3}{4}$