Algebra Examples

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

Step 1

Find the common denominator.

Tap for more steps...

Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

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

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

Step 1.6

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

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

Step 2

Combine the numerators over the common denominator.

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

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

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

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

Step 3.2

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

Tap for more steps...

Step 3.2.1

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

Tap for more steps...

Step 3.2.1.1

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

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

Step 3.2.1.2

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

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

Step 3.2.2

Add $1$ and $3$ .

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

Step 3.3

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

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

Step 3.4

Multiply $4$ by $1$ .

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

Step 3.5

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

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

Step 3.6

Multiply $3 \cdot 1 \cdot 4$ .

Tap for more steps...

Step 3.6.1

Multiply $3$ by $1$ .

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

Step 3.6.2

Multiply $3$ by $4$ .

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

Step 4

Simplify by adding numbers.

Tap for more steps...

Step 4.1

Add $1$ and $4$ .

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

Step 4.2

Add $5$ and $12$ .

$\frac{17}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{4}$

Decimal Form:

$4.25$

Mixed Number Form:

$4 \frac{1}{4}$