Algebra Examples

$\frac{2^{2}}{5} + {(\frac{2}{5})}^{2} - \frac{2^{0}}{5} + {(\frac{2}{5})}^{0}$

Step 1

Combine the numerators over the common denominator.

${(\frac{2}{5})}^{2} + {(\frac{2}{5})}^{0} + \frac{2^{2} - 2^{0}}{5}$

Step 2

Simplify each term.

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Step 2.1

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

${(\frac{2}{5})}^{2} + {(\frac{2}{5})}^{0} + \frac{4 - 2^{0}}{5}$

Step 2.2

Anything raised to $0$ is $1$ .

${(\frac{2}{5})}^{2} + {(\frac{2}{5})}^{0} + \frac{4 - 1 \cdot 1}{5}$

Step 2.3

Multiply $- 1$ by $1$ .

${(\frac{2}{5})}^{2} + {(\frac{2}{5})}^{0} + \frac{4 - 1}{5}$

Step 3

Subtract $1$ from $4$ .

${(\frac{2}{5})}^{2} + {(\frac{2}{5})}^{0} + \frac{3}{5}$

Step 4

Find the common denominator.

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Step 4.1

Write ${(\frac{2}{5})}^{2}$ as a fraction with denominator $1$ .

$\frac{{(\frac{2}{5})}^{2}}{1} + {(\frac{2}{5})}^{0} + \frac{3}{5}$

Step 4.2

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

$\frac{{(\frac{2}{5})}^{2}}{1} \cdot \frac{5}{5} + {(\frac{2}{5})}^{0} + \frac{3}{5}$

Step 4.3

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

$\frac{{(\frac{2}{5})}^{2} \cdot 5}{5} + {(\frac{2}{5})}^{0} + \frac{3}{5}$

Step 4.4

Write ${(\frac{2}{5})}^{0}$ as a fraction with denominator $1$ .

$\frac{{(\frac{2}{5})}^{2} \cdot 5}{5} + \frac{{(\frac{2}{5})}^{0}}{1} + \frac{3}{5}$

Step 4.5

Multiply $\frac{{(\frac{2}{5})}^{0}}{1}$ by $\frac{5}{5}$ .

$\frac{{(\frac{2}{5})}^{2} \cdot 5}{5} + \frac{{(\frac{2}{5})}^{0}}{1} \cdot \frac{5}{5} + \frac{3}{5}$

Step 4.6

Multiply $\frac{{(\frac{2}{5})}^{0}}{1}$ by $\frac{5}{5}$ .

$\frac{{(\frac{2}{5})}^{2} \cdot 5}{5} + \frac{{(\frac{2}{5})}^{0} \cdot 5}{5} + \frac{3}{5}$

Step 5

Combine the numerators over the common denominator.

$\frac{{(\frac{2}{5})}^{2} \cdot 5 + {(\frac{2}{5})}^{0} \cdot 5 + 3}{5}$

Step 6

Simplify each term.

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Step 6.1

Apply the product rule to $\frac{2}{5}$ .

$\frac{\frac{2^{2}}{5^{2}} \cdot 5 + {(\frac{2}{5})}^{0} \cdot 5 + 3}{5}$

Step 6.2

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

$\frac{\frac{4}{5^{2}} \cdot 5 + {(\frac{2}{5})}^{0} \cdot 5 + 3}{5}$

Step 6.3

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

$\frac{\frac{4}{25} \cdot 5 + {(\frac{2}{5})}^{0} \cdot 5 + 3}{5}$

Step 6.4

Cancel the common factor of $5$ .

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Step 6.4.1

Factor $5$ out of $25$ .

$\frac{\frac{4}{5 (5)} \cdot 5 + {(\frac{2}{5})}^{0} \cdot 5 + 3}{5}$

Step 6.4.2

Cancel the common factor.

$\frac{\frac{4}{5 \cdot 5} \cdot 5 + {(\frac{2}{5})}^{0} \cdot 5 + 3}{5}$

Step 6.4.3

Rewrite the expression.

$\frac{\frac{4}{5} + {(\frac{2}{5})}^{0} \cdot 5 + 3}{5}$

Step 6.5

Apply the product rule to $\frac{2}{5}$ .

$\frac{\frac{4}{5} + \frac{2^{0}}{5^{0}} \cdot 5 + 3}{5}$

Step 6.6

Anything raised to $0$ is $1$ .

$\frac{\frac{4}{5} + \frac{1}{5^{0}} \cdot 5 + 3}{5}$

Step 6.7

Anything raised to $0$ is $1$ .

$\frac{\frac{4}{5} + \frac{1}{1} \cdot 5 + 3}{5}$

Step 6.8

Cancel the common factor of $1$ .

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Step 6.8.1

Cancel the common factor.

$\frac{\frac{4}{5} + \frac{1}{1} \cdot 5 + 3}{5}$

Step 6.8.2

Rewrite the expression.

$\frac{\frac{4}{5} + 1 \cdot 5 + 3}{5}$

Step 6.9

Multiply $5$ by $1$ .

$\frac{\frac{4}{5} + 5 + 3}{5}$

Step 7

Find the common denominator.

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Step 7.1

Write $5$ as a fraction with denominator $1$ .

$\frac{\frac{4}{5} + \frac{5}{1} + 3}{5}$

Step 7.2

Multiply $\frac{5}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{4}{5} + \frac{5}{1} \cdot \frac{5}{5} + 3}{5}$

Step 7.3

Multiply $\frac{5}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{4}{5} + \frac{5 \cdot 5}{5} + 3}{5}$

Step 7.4

Write $3$ as a fraction with denominator $1$ .

$\frac{\frac{4}{5} + \frac{5 \cdot 5}{5} + \frac{3}{1}}{5}$

Step 7.5

Multiply $\frac{3}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{4}{5} + \frac{5 \cdot 5}{5} + \frac{3}{1} \cdot \frac{5}{5}}{5}$

Step 7.6

Multiply $\frac{3}{1}$ by $\frac{5}{5}$ .

$\frac{\frac{4}{5} + \frac{5 \cdot 5}{5} + \frac{3 \cdot 5}{5}}{5}$

Step 8

Combine the numerators over the common denominator.

$\frac{\frac{4 + 5 \cdot 5 + 3 \cdot 5}{5}}{5}$

Step 9

Simplify each term.

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Step 9.1

Multiply $5$ by $5$ .

$\frac{\frac{4 + 25 + 3 \cdot 5}{5}}{5}$

Step 9.2

Multiply $3$ by $5$ .

$\frac{\frac{4 + 25 + 15}{5}}{5}$

Step 10

Simplify by adding numbers.

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Step 10.1

Add $4$ and $25$ .

$\frac{\frac{29 + 15}{5}}{5}$

Step 10.2

Add $29$ and $15$ .

$\frac{\frac{44}{5}}{5}$

Step 11

Multiply the numerator by the reciprocal of the denominator.

$\frac{44}{5} \cdot \frac{1}{5}$

Step 12

Multiply $\frac{44}{5} \cdot \frac{1}{5}$ .

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Step 12.1

Multiply $\frac{44}{5}$ by $\frac{1}{5}$ .

$\frac{44}{5 \cdot 5}$

Step 12.2

Multiply $5$ by $5$ .

$\frac{44}{25}$

Step 13

The result can be shown in multiple forms.

Exact Form:

$\frac{44}{25}$

Decimal Form:

$1.76$

Mixed Number Form:

$1 \frac{19}{25}$