Finite Math Examples

$\frac{- 2^{3 + \sqrt{6 - 2}}}{| 3 (6) - (- 2) |}$

Step 1

Simplify the numerator.

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Step 1.1

Simplify each term.

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Step 1.1.1

Subtract $2$ from $6$ .

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

Step 1.1.2

Rewrite $4$ as $2^{2}$ .

$\frac{- 2^{3 + \sqrt{2^{2}}}}{| 3 (6) - (- 2) |}$

Step 1.1.3

Pull terms out from under the radical, assuming positive real numbers.

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

Step 1.2

Add $3$ and $2$ .

$\frac{- 2^{5}}{| 3 (6) - (- 2) |}$

Step 1.3

Raise $2$ to the power of $5$ .

$\frac{- 1 \cdot 32}{| 3 (6) - (- 2) |}$

Step 2

Simplify the denominator.

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Step 2.1

Multiply $3$ by $6$ .

$\frac{- 1 \cdot 32}{| 18 - (- 2) |}$

Step 2.2

Multiply $- 1$ by $- 2$ .

$\frac{- 1 \cdot 32}{| 18 + 2 |}$

Step 2.3

Add $18$ and $2$ .

$\frac{- 1 \cdot 32}{| 20 |}$

Step 2.4

The absolute value is the distance between a number and zero. The distance between $0$ and $20$ is $20$ .

$\frac{- 1 \cdot 32}{20}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Multiply $- 1$ by $32$ .

$\frac{- 32}{20}$

Step 3.2

Cancel the common factor of $- 32$ and $20$ .

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Step 3.2.1

Factor $4$ out of $- 32$ .

$\frac{4 (- 8)}{20}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $4$ out of $20$ .

$\frac{4 \cdot - 8}{4 \cdot 5}$

Step 3.2.2.2

Cancel the common factor.

$\frac{4 \cdot - 8}{4 \cdot 5}$

Step 3.2.2.3

Rewrite the expression.

$\frac{- 8}{5}$

Step 3.3

Move the negative in front of the fraction.

$- \frac{8}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{8}{5}$

Decimal Form:

$- 1.6$

Mixed Number Form:

$- 1 \frac{3}{5}$