Calculus Examples

$\frac{8}{3} \cdot {(\frac{1}{8})}^{3} - \frac{33}{2} \cdot {(\frac{1}{8})}^{2} + 4 (\frac{1}{8}) + 3$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $\frac{1}{8}$ .

$\frac{8}{3} \cdot \frac{1^{3}}{8^{3}} - \frac{33}{2} \cdot {(\frac{1}{8})}^{2} + 4 (\frac{1}{8}) + 3$

Step 1.2

Combine.

$\frac{8 \cdot 1^{3}}{3 \cdot 8^{3}} - \frac{33}{2} \cdot {(\frac{1}{8})}^{2} + 4 (\frac{1}{8}) + 3$

Step 1.3

Cancel the common factor of $8$ and $8^{3}$ .

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Step 1.3.1

Factor $8$ out of $8 \cdot 1^{3}$ .

$\frac{8 (1^{3})}{3 \cdot 8^{3}} - \frac{33}{2} \cdot {(\frac{1}{8})}^{2} + 4 (\frac{1}{8}) + 3$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $8$ out of $3 \cdot 8^{3}$ .

$\frac{8 (1^{3})}{8 (3 \cdot 8^{2})} - \frac{33}{2} \cdot {(\frac{1}{8})}^{2} + 4 (\frac{1}{8}) + 3$

Step 1.3.2.2

Cancel the common factor.

$\frac{8 \cdot 1^{3}}{8 (3 \cdot 8^{2})} - \frac{33}{2} \cdot {(\frac{1}{8})}^{2} + 4 (\frac{1}{8}) + 3$

Step 1.3.2.3

Rewrite the expression.

$\frac{1^{3}}{3 \cdot 8^{2}} - \frac{33}{2} \cdot {(\frac{1}{8})}^{2} + 4 (\frac{1}{8}) + 3$

Step 1.4

One to any power is one.

$\frac{1}{3 \cdot 8^{2}} - \frac{33}{2} \cdot {(\frac{1}{8})}^{2} + 4 (\frac{1}{8}) + 3$

Step 1.5

Raise $8$ to the power of $2$ .

$\frac{1}{3 \cdot 64} - \frac{33}{2} \cdot {(\frac{1}{8})}^{2} + 4 (\frac{1}{8}) + 3$

Step 1.6

Multiply $3$ by $64$ .

$\frac{1}{192} - \frac{33}{2} \cdot {(\frac{1}{8})}^{2} + 4 (\frac{1}{8}) + 3$

Step 1.7

Apply the product rule to $\frac{1}{8}$ .

$\frac{1}{192} - \frac{33}{2} \cdot \frac{1^{2}}{8^{2}} + 4 (\frac{1}{8}) + 3$

Step 1.8

One to any power is one.

$\frac{1}{192} - \frac{33}{2} \cdot \frac{1}{8^{2}} + 4 (\frac{1}{8}) + 3$

Step 1.9

Raise $8$ to the power of $2$ .

$\frac{1}{192} - \frac{33}{2} \cdot \frac{1}{64} + 4 (\frac{1}{8}) + 3$

Step 1.10

Multiply $- \frac{33}{2} \cdot \frac{1}{64}$ .

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Step 1.10.1

Multiply $\frac{1}{64}$ by $\frac{33}{2}$ .

$\frac{1}{192} - \frac{33}{64 \cdot 2} + 4 (\frac{1}{8}) + 3$

Step 1.10.2

Multiply $64$ by $2$ .

$\frac{1}{192} - \frac{33}{128} + 4 (\frac{1}{8}) + 3$

Step 1.11

Cancel the common factor of $4$ .

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Step 1.11.1

Factor $4$ out of $8$ .

$\frac{1}{192} - \frac{33}{128} + 4 \frac{1}{4 (2)} + 3$

Step 1.11.2

Cancel the common factor.

$\frac{1}{192} - \frac{33}{128} + 4 \frac{1}{4 \cdot 2} + 3$

Step 1.11.3

Rewrite the expression.

$\frac{1}{192} - \frac{33}{128} + \frac{1}{2} + 3$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{1}{192}$ by $\frac{2}{2}$ .

$\frac{1}{192} \cdot \frac{2}{2} - \frac{33}{128} + \frac{1}{2} + 3$

Step 2.2

Multiply $\frac{1}{192}$ by $\frac{2}{2}$ .

$\frac{2}{192 \cdot 2} - \frac{33}{128} + \frac{1}{2} + 3$

Step 2.3

Multiply $\frac{33}{128}$ by $\frac{3}{3}$ .

$\frac{2}{192 \cdot 2} - (\frac{33}{128} \cdot \frac{3}{3}) + \frac{1}{2} + 3$

Step 2.4

Multiply $\frac{33}{128}$ by $\frac{3}{3}$ .

$\frac{2}{192 \cdot 2} - \frac{33 \cdot 3}{128 \cdot 3} + \frac{1}{2} + 3$

Step 2.5

Multiply $\frac{1}{2}$ by $\frac{192}{192}$ .

$\frac{2}{192 \cdot 2} - \frac{33 \cdot 3}{128 \cdot 3} + \frac{1}{2} \cdot \frac{192}{192} + 3$

Step 2.6

Multiply $\frac{1}{2}$ by $\frac{192}{192}$ .

$\frac{2}{192 \cdot 2} - \frac{33 \cdot 3}{128 \cdot 3} + \frac{192}{2 \cdot 192} + 3$

Step 2.7

Write $3$ as a fraction with denominator $1$ .

$\frac{2}{192 \cdot 2} - \frac{33 \cdot 3}{128 \cdot 3} + \frac{192}{2 \cdot 192} + \frac{3}{1}$

Step 2.8

Multiply $\frac{3}{1}$ by $\frac{384}{384}$ .

$\frac{2}{192 \cdot 2} - \frac{33 \cdot 3}{128 \cdot 3} + \frac{192}{2 \cdot 192} + \frac{3}{1} \cdot \frac{384}{384}$

Step 2.9

Multiply $\frac{3}{1}$ by $\frac{384}{384}$ .

$\frac{2}{192 \cdot 2} - \frac{33 \cdot 3}{128 \cdot 3} + \frac{192}{2 \cdot 192} + \frac{3 \cdot 384}{384}$

Step 2.10

Reorder the factors of $192 \cdot 2$ .

$\frac{2}{2 \cdot 192} - \frac{33 \cdot 3}{128 \cdot 3} + \frac{192}{2 \cdot 192} + \frac{3 \cdot 384}{384}$

Step 2.11

Multiply $2$ by $192$ .

$\frac{2}{384} - \frac{33 \cdot 3}{128 \cdot 3} + \frac{192}{2 \cdot 192} + \frac{3 \cdot 384}{384}$

Step 2.12

Reorder the factors of $128 \cdot 3$ .

$\frac{2}{384} - \frac{33 \cdot 3}{3 \cdot 128} + \frac{192}{2 \cdot 192} + \frac{3 \cdot 384}{384}$

Step 2.13

Multiply $3$ by $128$ .

$\frac{2}{384} - \frac{33 \cdot 3}{384} + \frac{192}{2 \cdot 192} + \frac{3 \cdot 384}{384}$

Step 2.14

Multiply $2$ by $192$ .

$\frac{2}{384} - \frac{33 \cdot 3}{384} + \frac{192}{384} + \frac{3 \cdot 384}{384}$

Step 3

Combine the numerators over the common denominator.

$\frac{2 - 33 \cdot 3 + 192 + 3 \cdot 384}{384}$

Step 4

Simplify each term.

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Step 4.1

Multiply $- 33$ by $3$ .

$\frac{2 - 99 + 192 + 3 \cdot 384}{384}$

Step 4.2

Multiply $3$ by $384$ .

$\frac{2 - 99 + 192 + 1152}{384}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Subtract $99$ from $2$ .

$\frac{- 97 + 192 + 1152}{384}$

Step 5.2

Add $- 97$ and $192$ .

$\frac{95 + 1152}{384}$

Step 5.3

Add $95$ and $1152$ .

$\frac{1247}{384}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1247}{384}$

Decimal Form:

$3.24739583 \dots$

Mixed Number Form:

$3 \frac{95}{384}$