Evaluate -1/3(-5)^2+4

$- \frac{1}{3} {(- 5)}^{2} + 4$

Step 1

Simplify each term.

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

$- \frac{1}{3} \cdot 25 + 4$

Multiply $- \frac{1}{3} \cdot 25$ .

Multiply $25$ by $- 1$ .

$- 25 (\frac{1}{3}) + 4$

Combine $- 25$ and $\frac{1}{3}$ .

$\frac{- 25}{3} + 4$

Move the negative in front of the fraction.

$- \frac{25}{3} + 4$

Step 2

To write $4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{25}{3} + 4 \cdot \frac{3}{3}$

Step 3

Combine $4$ and $\frac{3}{3}$ .

$- \frac{25}{3} + \frac{4 \cdot 3}{3}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 25 + 4 \cdot 3}{3}$

Step 5

Simplify the numerator.

Multiply $4$ by $3$ .

$\frac{- 25 + 12}{3}$

Add $- 25$ and $12$ .

$\frac{- 13}{3}$

Step 6

Move the negative in front of the fraction.

$- \frac{13}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{13}{3}$

Decimal Form:

$- 4.\overline{3}$

Mixed Number Form:

$- 4 \frac{1}{3}$