Evaluate -5(6/5)^2+17(6/5)

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

Step 1

Simplify each term.

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

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

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

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

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

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

Cancel the common factor of $5$ .

Factor $5$ out of $- 5$ .

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

Factor $5$ out of $25$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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

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

Multiply $17$ by $6$ .

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

Step 2

Combine fractions.

Combine the numerators over the common denominator.

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

Add $- 36$ and $102$ .

$\frac{66}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{66}{5}$

Decimal Form:

$13.2$

Mixed Number Form:

$13 \frac{1}{5}$