Basic Math Examples

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

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

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

$- 1$ .

$- 2$