Basic Math Examples

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Move the negative in front of the fraction.

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

Step 3

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

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Step 3.1

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

${(- 1)}^{2} {(\frac{3}{5})}^{2} (- \frac{10}{3})$

Step 3.2

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

${(- 1)}^{2} \frac{3^{2}}{5^{2}} (- \frac{10}{3})$

Step 4

Multiply ${(- 1)}^{2}$ by $- 1$ by adding the exponents.

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Step 4.1

Move $- 1$ .

$- {(- 1)}^{2} \frac{3^{2}}{5^{2}} \frac{10}{3}$

Step 4.2

Multiply $- 1$ by ${(- 1)}^{2}$ .

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Step 4.2.1

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

${(- 1)}^{1} {(- 1)}^{2} \frac{3^{2}}{5^{2}} \frac{10}{3}$

Step 4.2.2

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

${(- 1)}^{1 + 2} \frac{3^{2}}{5^{2}} \frac{10}{3}$

Step 4.3

Add $1$ and $2$ .

${(- 1)}^{3} \frac{3^{2}}{5^{2}} \frac{10}{3}$

Step 5

Evaluate the exponents.

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Step 5.1

Raise $- 1$ to the power of $3$ .

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

Step 5.2

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

$- \frac{9}{5^{2}} \cdot \frac{10}{3}$

Step 5.3

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

$- \frac{9}{25} \cdot \frac{10}{3}$

Step 6

Cancel the common factor of $3$ .

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Step 6.1

Move the leading negative in $- \frac{9}{25}$ into the numerator.

$\frac{- 9}{25} \cdot \frac{10}{3}$

Step 6.2

Factor $3$ out of $- 9$ .

$\frac{3 (- 3)}{25} \cdot \frac{10}{3}$

Step 6.3

Cancel the common factor.

$\frac{3 \cdot - 3}{25} \cdot \frac{10}{3}$

Step 6.4

Rewrite the expression.

$\frac{- 3}{25} \cdot 10$

Step 7

Cancel the common factor of $5$ .

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Step 7.1

Factor $5$ out of $25$ .

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

Step 7.2

Factor $5$ out of $10$ .

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

Step 7.3

Cancel the common factor.

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

Step 7.4

Rewrite the expression.

$\frac{- 3}{5} \cdot 2$

Step 8

Combine $\frac{- 3}{5}$ and $2$ .

$\frac{- 3 \cdot 2}{5}$

Step 9

Simplify the expression.

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Step 9.1

Multiply $- 3$ by $2$ .

$\frac{- 6}{5}$

Step 9.2

Move the negative in front of the fraction.

$- \frac{6}{5}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \frac{6}{5}$

Decimal Form:

$- 1.2$

Mixed Number Form:

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