Finite Math Examples

$3 \cdot ((\frac{11}{30}) {(1 - \frac{11}{30})}^{2})$

Step 1

Simplify the expression.

Tap for more steps...

Step 1.1

Write $1$ as a fraction with a common denominator.

$3 \cdot (\frac{11}{30} {(\frac{30}{30} - \frac{11}{30})}^{2})$

Step 1.2

Combine the numerators over the common denominator.

$3 \cdot (\frac{11}{30} {(\frac{30 - 11}{30})}^{2})$

Step 1.3

Subtract $11$ from $30$ .

$3 \cdot (\frac{11}{30} {(\frac{19}{30})}^{2})$

Step 1.4

Apply the product rule to $\frac{19}{30}$ .

$3 \cdot (\frac{11}{30} \cdot \frac{19^{2}}{30^{2}})$

Step 2

Combine.

$3 \cdot \frac{11 \cdot 19^{2}}{30 \cdot 30^{2}}$

Step 3

Raise $19$ to the power of $2$ .

$3 \cdot \frac{11 \cdot 361}{30 \cdot 30^{2}}$

Step 4

Multiply $30$ by $30^{2}$ by adding the exponents.

Tap for more steps...

Step 4.1

Multiply $30$ by $30^{2}$ .

Tap for more steps...

Step 4.1.1

Raise $30$ to the power of $1$ .

$3 \cdot \frac{11 \cdot 361}{30^{1} \cdot 30^{2}}$

Step 4.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 \cdot \frac{11 \cdot 361}{30^{1 + 2}}$

Step 4.2

Add $1$ and $2$ .

$3 \cdot \frac{11 \cdot 361}{30^{3}}$

Step 5

Simplify the expression.

Tap for more steps...

Step 5.1

Multiply $11$ by $361$ .

$3 \cdot \frac{3971}{30^{3}}$

Step 5.2

Raise $30$ to the power of $3$ .

$3 \cdot \frac{3971}{27000}$

Step 6

Cancel the common factor of $3$ .

Tap for more steps...

Step 6.1

Factor $3$ out of $27000$ .

$3 \cdot \frac{3971}{3 (9000)}$

Step 6.2

Cancel the common factor.

$3 \cdot \frac{3971}{3 \cdot 9000}$

Step 6.3

Rewrite the expression.

$\frac{3971}{9000}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{3971}{9000}$

Decimal Form:

$0.441\overline{2}$