Basic Math Examples

$\frac{{(2)}^{4}}{4} - \frac{4 \cdot {(2)}^{3}}{3} + \frac{{(2)}^{2}}{2} + 6 \cdot (2)$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{{(2)}^{4}}{4}$ by $\frac{3}{3}$ .

$\frac{{(2)}^{4}}{4} \cdot \frac{3}{3} - \frac{4 \cdot {(2)}^{3}}{3} + \frac{{(2)}^{2}}{2} + 6 \cdot (2)$

Step 1.2

Multiply $\frac{{(2)}^{4}}{4}$ by $\frac{3}{3}$ .

$\frac{{(2)}^{4} \cdot 3}{4 \cdot 3} - \frac{4 \cdot {(2)}^{3}}{3} + \frac{{(2)}^{2}}{2} + 6 \cdot (2)$

Step 1.3

Multiply $\frac{4 \cdot {(2)}^{3}}{3}$ by $\frac{4}{4}$ .

$\frac{{(2)}^{4} \cdot 3}{4 \cdot 3} - (\frac{4 \cdot {(2)}^{3}}{3} \cdot \frac{4}{4}) + \frac{{(2)}^{2}}{2} + 6 \cdot (2)$

Step 1.4

Multiply $\frac{4 \cdot {(2)}^{3}}{3}$ by $\frac{4}{4}$ .

$\frac{{(2)}^{4} \cdot 3}{4 \cdot 3} - \frac{4 \cdot {(2)}^{3} \cdot 4}{3 \cdot 4} + \frac{{(2)}^{2}}{2} + 6 \cdot (2)$

Step 1.5

Multiply $\frac{{(2)}^{2}}{2}$ by $\frac{6}{6}$ .

$\frac{{(2)}^{4} \cdot 3}{4 \cdot 3} - \frac{4 \cdot {(2)}^{3} \cdot 4}{3 \cdot 4} + \frac{{(2)}^{2}}{2} \cdot \frac{6}{6} + 6 \cdot (2)$

Step 1.6

Multiply $\frac{{(2)}^{2}}{2}$ by $\frac{6}{6}$ .

$\frac{{(2)}^{4} \cdot 3}{4 \cdot 3} - \frac{4 \cdot {(2)}^{3} \cdot 4}{3 \cdot 4} + \frac{{(2)}^{2} \cdot 6}{2 \cdot 6} + 6 \cdot (2)$

Step 1.7

Write $6 \cdot (2)$ as a fraction with denominator $1$ .

$\frac{{(2)}^{4} \cdot 3}{4 \cdot 3} - \frac{4 \cdot {(2)}^{3} \cdot 4}{3 \cdot 4} + \frac{{(2)}^{2} \cdot 6}{2 \cdot 6} + \frac{6 \cdot (2)}{1}$

Step 1.8

Multiply $\frac{6 \cdot (2)}{1}$ by $\frac{12}{12}$ .

$\frac{{(2)}^{4} \cdot 3}{4 \cdot 3} - \frac{4 \cdot {(2)}^{3} \cdot 4}{3 \cdot 4} + \frac{{(2)}^{2} \cdot 6}{2 \cdot 6} + \frac{6 \cdot (2)}{1} \cdot \frac{12}{12}$

Step 1.9

Multiply $\frac{6 \cdot (2)}{1}$ by $\frac{12}{12}$ .

$\frac{{(2)}^{4} \cdot 3}{4 \cdot 3} - \frac{4 \cdot {(2)}^{3} \cdot 4}{3 \cdot 4} + \frac{{(2)}^{2} \cdot 6}{2 \cdot 6} + \frac{6 \cdot (2) \cdot 12}{12}$

Step 1.10

Reorder the factors of $4 \cdot 3$ .

$\frac{{(2)}^{4} \cdot 3}{3 \cdot 4} - \frac{4 \cdot {(2)}^{3} \cdot 4}{3 \cdot 4} + \frac{{(2)}^{2} \cdot 6}{2 \cdot 6} + \frac{6 \cdot (2) \cdot 12}{12}$

Step 1.11

Multiply $3$ by $4$ .

$\frac{{(2)}^{4} \cdot 3}{12} - \frac{4 \cdot {(2)}^{3} \cdot 4}{3 \cdot 4} + \frac{{(2)}^{2} \cdot 6}{2 \cdot 6} + \frac{6 \cdot (2) \cdot 12}{12}$

Step 1.12

Multiply $3$ by $4$ .

$\frac{{(2)}^{4} \cdot 3}{12} - \frac{4 \cdot {(2)}^{3} \cdot 4}{12} + \frac{{(2)}^{2} \cdot 6}{2 \cdot 6} + \frac{6 \cdot (2) \cdot 12}{12}$

Step 1.13

Multiply $2$ by $6$ .

$\frac{{(2)}^{4} \cdot 3}{12} - \frac{4 \cdot {(2)}^{3} \cdot 4}{12} + \frac{{(2)}^{2} \cdot 6}{12} + \frac{6 \cdot (2) \cdot 12}{12}$

Step 2

Combine the numerators over the common denominator.

$\frac{{(2)}^{4} \cdot 3 - 4 \cdot {(2)}^{3} \cdot 4 + {(2)}^{2} \cdot 6 + 6 \cdot (2) \cdot 12}{12}$

Step 3

Simplify each term.

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Step 3.1

Raise $2$ to the power of $4$ .

$\frac{16 \cdot 3 - 4 \cdot {(2)}^{3} \cdot 4 + {(2)}^{2} \cdot 6 + 6 \cdot (2) \cdot 12}{12}$

Step 3.2

Multiply $16$ by $3$ .

$\frac{48 - 4 \cdot {(2)}^{3} \cdot 4 + {(2)}^{2} \cdot 6 + 6 \cdot (2) \cdot 12}{12}$

Step 3.3

Raise $2$ to the power of $3$ .

$\frac{48 - 4 \cdot 8 \cdot 4 + {(2)}^{2} \cdot 6 + 6 \cdot (2) \cdot 12}{12}$

Step 3.4

Multiply $- 4 \cdot 8 \cdot 4$ .

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Step 3.4.1

Multiply $- 4$ by $8$ .

$\frac{48 - 32 \cdot 4 + {(2)}^{2} \cdot 6 + 6 \cdot (2) \cdot 12}{12}$

Step 3.4.2

Multiply $- 32$ by $4$ .

$\frac{48 - 128 + {(2)}^{2} \cdot 6 + 6 \cdot (2) \cdot 12}{12}$

Step 3.5

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

$\frac{48 - 128 + 4 \cdot 6 + 6 \cdot (2) \cdot 12}{12}$

Step 3.6

Multiply $4$ by $6$ .

$\frac{48 - 128 + 24 + 6 \cdot (2) \cdot 12}{12}$

Step 3.7

Multiply $6 \cdot (2) \cdot 12$ .

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Step 3.7.1

Multiply $6$ by $2$ .

$\frac{48 - 128 + 24 + 12 \cdot 12}{12}$

Step 3.7.2

Multiply $12$ by $12$ .

$\frac{48 - 128 + 24 + 144}{12}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Subtract $128$ from $48$ .

$\frac{- 80 + 24 + 144}{12}$

Step 4.2

Simplify by adding numbers.

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Step 4.2.1

Add $- 80$ and $24$ .

$\frac{- 56 + 144}{12}$

Step 4.2.2

Add $- 56$ and $144$ .

$\frac{88}{12}$

Step 4.3

Cancel the common factor of $88$ and $12$ .

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Step 4.3.1

Factor $4$ out of $88$ .

$\frac{4 (22)}{12}$

Step 4.3.2

Cancel the common factors.

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Step 4.3.2.1

Factor $4$ out of $12$ .

$\frac{4 \cdot 22}{4 \cdot 3}$

Step 4.3.2.2

Cancel the common factor.

$\frac{4 \cdot 22}{4 \cdot 3}$

Step 4.3.2.3

Rewrite the expression.

$\frac{22}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{22}{3}$

Decimal Form:

$7.\overline{3}$

Mixed Number Form:

$7 \frac{1}{3}$