Basic Math Examples

$- 5 {(- \frac{6}{5})}^{2} + 17 (- \frac{6}{5})$

Step 1

Simplify each term.

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Step 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

Apply the product rule to $- \frac{6}{5}$ .

$- 5 ({(- 1)}^{2} {(\frac{6}{5})}^{2}) + 17 (- \frac{6}{5})$

Step 1.1.2

Apply the product rule to $\frac{6}{5}$ .

$- 5 ({(- 1)}^{2} \frac{6^{2}}{5^{2}}) + 17 (- \frac{6}{5})$

Step 1.2

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

$- 5 (1 \frac{6^{2}}{5^{2}}) + 17 (- \frac{6}{5})$

Step 1.3

Multiply $\frac{6^{2}}{5^{2}}$ by $1$ .

$- 5 \frac{6^{2}}{5^{2}} + 17 (- \frac{6}{5})$

Step 1.4

Raise $6$ to the power of $2$ .

$- 5 \frac{36}{5^{2}} + 17 (- \frac{6}{5})$

Step 1.5

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

$- 5 (\frac{36}{25}) + 17 (- \frac{6}{5})$

Step 1.6

Cancel the common factor of $5$ .

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Step 1.6.1

Factor $5$ out of $- 5$ .

$5 (- 1) \frac{36}{25} + 17 (- \frac{6}{5})$

Step 1.6.2

Factor $5$ out of $25$ .

$5 \cdot - 1 \frac{36}{5 \cdot 5} + 17 (- \frac{6}{5})$

Step 1.6.3

Cancel the common factor.

$5 \cdot - 1 \frac{36}{5 \cdot 5} + 17 (- \frac{6}{5})$

Step 1.6.4

Rewrite the expression.

$- 1 (\frac{36}{5}) + 17 (- \frac{6}{5})$

Step 1.7

Rewrite $- 1 (\frac{36}{5})$ as $- (\frac{36}{5})$ .

$- (\frac{36}{5}) + 17 (- \frac{6}{5})$

Step 1.8

Multiply $17 (- \frac{6}{5})$ .

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Step 1.8.1

Multiply $- 1$ by $17$ .

$- \frac{36}{5} - 17 (\frac{6}{5})$

Step 1.8.2

Combine $- 17$ and $\frac{6}{5}$ .

$- \frac{36}{5} + \frac{- 17 \cdot 6}{5}$

Step 1.8.3

Multiply $- 17$ by $6$ .

$- \frac{36}{5} + \frac{- 102}{5}$

Step 1.9

Move the negative in front of the fraction.

$- \frac{36}{5} - \frac{102}{5}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{- 36 - 102}{5}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Subtract $102$ from $- 36$ .

$\frac{- 138}{5}$

Step 2.2.2

Move the negative in front of the fraction.

$- \frac{138}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{138}{5}$

Decimal Form:

$- 27.6$

Mixed Number Form:

$- 27 \frac{3}{5}$