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

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

Find the common denominator.

Write $- {(- 1)}^{3}$ as a fraction with denominator $1$ .

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

Multiply $\frac{- {(- 1)}^{3}}{1}$ by $\frac{4}{4}$ .

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

Multiply $\frac{- {(- 1)}^{3}}{1}$ by $\frac{4}{4}$ .

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

Write $3 {(- 1)}^{2}$ as a fraction with denominator $1$ .

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

Multiply $\frac{3 {(- 1)}^{2}}{1}$ by $\frac{4}{4}$ .

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

Multiply $\frac{3 {(- 1)}^{2}}{1}$ by $\frac{4}{4}$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Raise $- 1$ to the power of $4$ .

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

Multiply $- 1$ by ${(- 1)}^{3}$ by adding the exponents.

Multiply $- 1$ by ${(- 1)}^{3}$ .

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

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

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

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

Add $1$ and $3$ .

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

Raise $- 1$ to the power of $4$ .

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

Multiply $4$ by $1$ .

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

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

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

Multiply $3$ by $1$ .

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

Multiply $3$ by $4$ .

$\frac{1 + 4 + 12}{4}$

Simplify by adding numbers.

Add $1$ and $4$ .

$\frac{5 + 12}{4}$

Add $5$ and $12$ .

$\frac{17}{4}$

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{4}$

Decimal Form:

$4.25$

Mixed Number Form:

$4 \frac{1}{4}$

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

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