Basic Math Examples

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

Step 1

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 2

To write $- \frac{6}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{3}{2}$ by $\frac{5}{5}$ .

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

Step 3.2

Multiply $2$ by $5$ .

${(- 2 \cdot (\frac{3 \cdot 5}{10} - \frac{6}{5} \cdot \frac{2}{2}))}^{2}$

Step 3.3

Multiply $\frac{6}{5}$ by $\frac{2}{2}$ .

${(- 2 \cdot (\frac{3 \cdot 5}{10} - \frac{6 \cdot 2}{5 \cdot 2}))}^{2}$

Step 3.4

Multiply $5$ by $2$ .

${(- 2 \cdot (\frac{3 \cdot 5}{10} - \frac{6 \cdot 2}{10}))}^{2}$

Step 4

Combine the numerators over the common denominator.

${(- 2 \cdot \frac{3 \cdot 5 - 6 \cdot 2}{10})}^{2}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $5$ .

${(- 2 \cdot \frac{15 - 6 \cdot 2}{10})}^{2}$

Step 5.2

Multiply $- 6$ by $2$ .

${(- 2 \cdot \frac{15 - 12}{10})}^{2}$

Step 5.3

Subtract $12$ from $15$ .

${(- 2 \cdot \frac{3}{10})}^{2}$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Factor $2$ out of $- 2$ .

${(2 (- 1) \cdot \frac{3}{10})}^{2}$

Step 6.2

Factor $2$ out of $10$ .

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

Step 6.3

Cancel the common factor.

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

Step 6.4

Rewrite the expression.

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

Step 7

Rewrite $- 1 (\frac{3}{5})$ as $- (\frac{3}{5})$ .

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

Step 8

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

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Step 8.1

Apply the product rule to $- \frac{3}{5}$ .

${(- 1)}^{2} {(\frac{3}{5})}^{2}$

Step 8.2

Apply the product rule to $\frac{3}{5}$ .

${(- 1)}^{2} \frac{3^{2}}{5^{2}}$

Step 9

Raise $- 1$ to the power of $2$ .

$1 \frac{3^{2}}{5^{2}}$

Step 10

Multiply $\frac{3^{2}}{5^{2}}$ by $1$ .

$\frac{3^{2}}{5^{2}}$

Step 11

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

$\frac{9}{5^{2}}$

Step 12

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

$\frac{9}{25}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{25}$

Decimal Form:

$0.36$