Basic Math Examples

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

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

Step 1

Raise

3

$3$ to the power of

2

$2$ .

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

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

Step 2

Simplify the numerator.

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Step 2.1

Raise

4

$4$ to the power of

3

$3$ .

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

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

Step 2.2

Multiply

- 1

$- 1$ by

64

$64$ .

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

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

Step 2.3

Raise

4

$4$ to the power of

2

$2$ .

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

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

Step 2.4

Multiply

- 9

$- 9$ by

16

$16$ .

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

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

Step 2.5

Subtract

144

$144$ from

- 64

$- 64$ .

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

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

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

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

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

$14$ from

2

$2$ .

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

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

Step 3.1.2

The absolute value is the distance between a number and zero. The distance between

- 12

$- 12$ and

0

$0$ is

12

$12$ .

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

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

Step 3.1.3

Multiply

- 1

$- 1$ by

12

$12$ .

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

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

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

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

Step 3.2

Subtract

12

$12$ from

4

$4$ .

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

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

Step 3.3

Multiply

- 1

$- 1$ by

- 8

$- 8$ .

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

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

Step 3.4

To write

8

$8$ as a fraction with a common denominator, multiply by

\frac{9}{9}

$\frac{9}{9}$ .

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

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

Step 3.5

Combine

8

$8$ and

\frac{9}{9}

$\frac{9}{9}$ .

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

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

Step 3.7

Simplify the numerator.

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Step 3.7.1

Multiply

8

$8$ by

9

$9$ .

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

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

Step 3.7.2

Add

45

$45$ and

72

$72$ .

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

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

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

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

Step 3.8

Divide

117

$117$ by

9

$9$ .

\frac{- 208}{13}

$\frac{- 208}{13}$

\frac{- 208}{13}

$\frac{- 208}{13}$

Step 4

Divide

- 208

$- 208$ by

13

$13$ .

- 16

$- 16$