Basic Math Examples

$\frac{(- 2^{2}) \cdot (- 5) + | - 2 | \cdot (- 3^{2})}{{(- 2)}^{3} - {(- 3)}^{2} + | - 4^{2} |}$

Step 1

Simplify the numerator.

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Step 1.1

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

$\frac{- 1 \cdot 4 \cdot - 5 + | - 2 | \cdot - 1 \cdot 3^{2}}{{(- 2)}^{3} - {(- 3)}^{2} + | - 4^{2} |}$

Step 1.2

Multiply $- 1 \cdot 4 \cdot - 5$ .

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Step 1.2.1

Multiply $- 1$ by $4$ .

$\frac{- 4 \cdot - 5 + | - 2 | \cdot - 1 \cdot 3^{2}}{{(- 2)}^{3} - {(- 3)}^{2} + | - 4^{2} |}$

Step 1.2.2

Multiply $- 4$ by $- 5$ .

$\frac{20 + | - 2 | \cdot - 1 \cdot 3^{2}}{{(- 2)}^{3} - {(- 3)}^{2} + | - 4^{2} |}$

Step 1.3

The absolute value is the distance between a number and zero. The distance between $- 2$ and $0$ is $2$ .

$\frac{20 + 2 \cdot - 1 \cdot 3^{2}}{{(- 2)}^{3} - {(- 3)}^{2} + | - 4^{2} |}$

Step 1.4

Multiply $2$ by $- 1$ .

$\frac{20 - 2 \cdot 3^{2}}{{(- 2)}^{3} - {(- 3)}^{2} + | - 4^{2} |}$

Step 1.5

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

$\frac{20 - 2 \cdot 9}{{(- 2)}^{3} - {(- 3)}^{2} + | - 4^{2} |}$

Step 1.6

Multiply $- 2$ by $9$ .

$\frac{20 - 18}{{(- 2)}^{3} - {(- 3)}^{2} + | - 4^{2} |}$

Step 1.7

Subtract $18$ from $20$ .

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

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{2}{- 8 - {(- 3)}^{2} + | - 4^{2} |}$

Step 2.2

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

$\frac{2}{- 8 - 1 \cdot 9 + | - 4^{2} |}$

Step 2.3

Multiply $- 1$ by $9$ .

$\frac{2}{- 8 - 9 + | - 4^{2} |}$

Step 2.4

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

$\frac{2}{- 8 - 9 + | - 1 \cdot 16 |}$

Step 2.5

Multiply $- 1$ by $16$ .

$\frac{2}{- 8 - 9 + | - 16 |}$

Step 2.6

The absolute value is the distance between a number and zero. The distance between $- 16$ and $0$ is $16$ .

$\frac{2}{- 8 - 9 + 16}$

Step 2.7

Subtract $9$ from $- 8$ .

$\frac{2}{- 17 + 16}$

Step 2.8

Add $- 17$ and $16$ .

$\frac{2}{- 1}$

Step 3

Divide $2$ by $- 1$ .

$- 2$