Finite Math Examples

$s \cdot 5 = \frac{224 ({(- \frac{3}{2})}^{5} - 1)}{- \frac{3}{2} - 1}$

Step 1

Simplify.

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Step 1.1

Simplify each term.

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Step 1.1.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1.1.1

Apply the product rule to $- \frac{3}{2}$ .

$s \cdot 5 = \frac{224 ({(- 1)}^{5} {(\frac{3}{2})}^{5} - 1)}{- \frac{3}{2} - 1}$

Step 1.1.1.2

Apply the product rule to $\frac{3}{2}$ .

$s \cdot 5 = \frac{224 ({(- 1)}^{5} \frac{3^{5}}{2^{5}} - 1)}{- \frac{3}{2} - 1}$

Step 1.1.2

Raise $- 1$ to the power of $5$ .

$s \cdot 5 = \frac{224 (- \frac{3^{5}}{2^{5}} - 1)}{- \frac{3}{2} - 1}$

Step 1.1.3

Raise $3$ to the power of $5$ .

$s \cdot 5 = \frac{224 (- \frac{243}{2^{5}} - 1)}{- \frac{3}{2} - 1}$

Step 1.1.4

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

$s \cdot 5 = \frac{224 (- \frac{243}{32} - 1)}{- \frac{3}{2} - 1}$

Step 1.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{32}{32}$ .

$s \cdot 5 = \frac{224 (- \frac{243}{32} - 1 \cdot \frac{32}{32})}{- \frac{3}{2} - 1}$

Step 1.3

Combine $- 1$ and $\frac{32}{32}$ .

$s \cdot 5 = \frac{224 (- \frac{243}{32} + \frac{- 1 \cdot 32}{32})}{- \frac{3}{2} - 1}$

Step 1.4

Combine the numerators over the common denominator.

$s \cdot 5 = \frac{224 \frac{- 243 - 1 \cdot 32}{32}}{- \frac{3}{2} - 1}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 1$ by $32$ .

$s \cdot 5 = \frac{224 \frac{- 243 - 32}{32}}{- \frac{3}{2} - 1}$

Step 1.5.2

Subtract $32$ from $- 243$ .

$s \cdot 5 = \frac{224 (\frac{- 275}{32})}{- \frac{3}{2} - 1}$

Step 1.6

Cancel the common factor of $32$ .

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Step 1.6.1

Factor $32$ out of $224$ .

$s \cdot 5 = \frac{32 (7) \frac{- 275}{32}}{- \frac{3}{2} - 1}$

Step 1.6.2

Cancel the common factor.

$s \cdot 5 = \frac{32 \cdot 7 \frac{- 275}{32}}{- \frac{3}{2} - 1}$

Step 1.6.3

Rewrite the expression.

$s \cdot 5 = \frac{7 \cdot - 275}{- \frac{3}{2} - 1}$

Step 1.7

Multiply $7$ by $- 275$ .

$s \cdot 5 = \frac{- 1925}{- \frac{3}{2} - 1}$

Step 1.8

Simplify the denominator.

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Step 1.8.1

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$s \cdot 5 = \frac{- 1925}{- \frac{3}{2} - 1 \cdot \frac{2}{2}}$

Step 1.8.2

Combine $- 1$ and $\frac{2}{2}$ .

$s \cdot 5 = \frac{- 1925}{- \frac{3}{2} + \frac{- 1 \cdot 2}{2}}$

Step 1.8.3

Combine the numerators over the common denominator.

$s \cdot 5 = \frac{- 1925}{\frac{- 3 - 1 \cdot 2}{2}}$

Step 1.8.4

Simplify the numerator.

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Step 1.8.4.1

Multiply $- 1$ by $2$ .

$s \cdot 5 = \frac{- 1925}{\frac{- 3 - 2}{2}}$

Step 1.8.4.2

Subtract $2$ from $- 3$ .

$s \cdot 5 = \frac{- 1925}{\frac{- 5}{2}}$

Step 1.8.5

Move the negative in front of the fraction.

$s \cdot 5 = \frac{- 1925}{- \frac{5}{2}}$

Step 1.9

Multiply the numerator by the reciprocal of the denominator.

$s \cdot 5 = - 1925 (- \frac{2}{5})$

Step 1.10

Cancel the common factor of $5$ .

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Step 1.10.1

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$s \cdot 5 = - 1925 (\frac{- 2}{5})$

Step 1.10.2

Factor $5$ out of $- 1925$ .

$s \cdot 5 = 5 (- 385) \frac{- 2}{5}$

Step 1.10.3

Cancel the common factor.

$s \cdot 5 = 5 \cdot - 385 \frac{- 2}{5}$

Step 1.10.4

Rewrite the expression.

$s \cdot 5 = - 385 \cdot - 2$

Step 1.11

Multiply $- 385$ by $- 2$ .

$s \cdot 5 = 770$

Step 2

Divide each term in $s \cdot 5 = 770$ by $5$ and simplify.

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Step 2.1

Divide each term in $s \cdot 5 = 770$ by $5$ .

$\frac{s \cdot 5}{5} = \frac{770}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{s \cdot 5}{5} = \frac{770}{5}$

Step 2.2.1.2

Divide $s$ by $1$ .

$s = \frac{770}{5}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $770$ by $5$ .

$s = 154$