Basic Math Examples

$\frac{- 4^{3} - 9 \cdot 4^{2}}{45 \div 3^{2} - (4 - | 2 - 14 |)}$

Step 1

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

$\frac{- 4^{3} - 9 \cdot 4^{2}}{45 \div 9 - (4 - | 2 - 14 |)}$

Step 2

Simplify the numerator.

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Step 2.1

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

$\frac{- 1 \cdot 64 - 9 \cdot 4^{2}}{45 \div 9 - (4 - | 2 - 14 |)}$

Step 2.2

Multiply $- 1$ by $64$ .

$\frac{- 64 - 9 \cdot 4^{2}}{45 \div 9 - (4 - | 2 - 14 |)}$

Step 2.3

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

$\frac{- 64 - 9 \cdot 16}{45 \div 9 - (4 - | 2 - 14 |)}$

Step 2.4

Multiply $- 9$ by $16$ .

$\frac{- 64 - 144}{45 \div 9 - (4 - | 2 - 14 |)}$

Step 2.5

Subtract $144$ from $- 64$ .

$\frac{- 208}{45 \div 9 - (4 - | 2 - 14 |)}$

Step 3

Simplify the denominator.

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Step 3.1

Simplify each term.

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Step 3.1.1

Subtract $14$ from $2$ .

$\frac{- 208}{45 \div 9 - (4 - | - 12 |)}$

Step 3.1.2

The absolute value is the distance between a number and zero. The distance between $- 12$ and $0$ is $12$ .

$\frac{- 208}{45 \div 9 - (4 - 1 \cdot 12)}$

Step 3.1.3

Multiply $- 1$ by $12$ .

$\frac{- 208}{45 \div 9 - (4 - 12)}$

Step 3.2

Subtract $12$ from $4$ .

$\frac{- 208}{45 \div 9 - - 8}$

Step 3.3

Multiply $- 1$ by $- 8$ .

$\frac{- 208}{45 \div 9 + 8}$

Step 3.4

To write $8$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{- 208}{45 \div 9 + 8 \cdot \frac{9}{9}}$

Step 3.5

Combine $8$ and $\frac{9}{9}$ .

$\frac{- 208}{45 \div 9 + \frac{8 \cdot 9}{9}}$

Step 3.6

Combine the numerators over the common denominator.

$\frac{- 208}{(45 + 8 \cdot 9) \div 9}$

Step 3.7

Simplify the numerator.

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Step 3.7.1

Multiply $8$ by $9$ .

$\frac{- 208}{(45 + 72) \div 9}$

Step 3.7.2

Add $45$ and $72$ .

$\frac{- 208}{117 \div 9}$

Step 3.8

Divide $117$ by $9$ .

$\frac{- 208}{13}$

Step 4

Divide $- 208$ by $13$ .

$- 16$