Basic Math Examples

${(0.16)}^{2} + {(\frac{1}{5})}^{2} (10)$

Step 1

Simplify each term.

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Step 1.1

Raise $0.16$ to the power of $2$ .

$0.0256 + {(\frac{1}{5})}^{2} (10)$

Step 1.2

Apply the product rule to $\frac{1}{5}$ .

$0.0256 + \frac{1^{2}}{5^{2}} \cdot 10$

Step 1.3

One to any power is one.

$0.0256 + \frac{1}{5^{2}} \cdot 10$

Step 1.4

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

$0.0256 + \frac{1}{25} \cdot 10$

Step 1.5

Cancel the common factor of $5$ .

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Step 1.5.1

Factor $5$ out of $25$ .

$0.0256 + \frac{1}{5 (5)} \cdot 10$

Step 1.5.2

Factor $5$ out of $10$ .

$0.0256 + \frac{1}{5 \cdot 5} \cdot (5 \cdot 2)$

Step 1.5.3

Cancel the common factor.

$0.0256 + \frac{1}{5 \cdot 5} \cdot (5 \cdot 2)$

Step 1.5.4

Rewrite the expression.

$0.0256 + \frac{1}{5} \cdot 2$

Step 1.6

Combine $\frac{1}{5}$ and $2$ .

$0.0256 + \frac{2}{5}$

Step 2

To write $0.0256$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$0.0256 \cdot \frac{5}{5} + \frac{2}{5}$

Step 3

Combine fractions.

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Step 3.1

Combine $0.0256$ and $\frac{5}{5}$ .

$\frac{0.0256 \cdot 5}{5} + \frac{2}{5}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{0.0256 \cdot 5 + 2}{5}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $0.0256$ by $5$ .

$\frac{0.128 + 2}{5}$

Step 4.2

Add $0.128$ and $2$ .

$\frac{2.128}{5}$

Step 5

Divide $2.128$ by $5$ .

$0.4256$