Basic Math Examples

${(\frac{2}{5})}^{3} + {(\frac{1}{10})}^{2} - {(\frac{1}{2})}^{3}$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{2^{3}}{5^{3}} + {(\frac{1}{10})}^{2} - {(\frac{1}{2})}^{3}$

Step 1.2

Raise $2$ to the power of $3$ .

$\frac{8}{5^{3}} + {(\frac{1}{10})}^{2} - {(\frac{1}{2})}^{3}$

Step 1.3

Raise $5$ to the power of $3$ .

$\frac{8}{125} + {(\frac{1}{10})}^{2} - {(\frac{1}{2})}^{3}$

Step 1.4

Apply the product rule to $\frac{1}{10}$ .

$\frac{8}{125} + \frac{1^{2}}{10^{2}} - {(\frac{1}{2})}^{3}$

Step 1.5

One to any power is one.

$\frac{8}{125} + \frac{1}{10^{2}} - {(\frac{1}{2})}^{3}$

Step 1.6

Raise $10$ to the power of $2$ .

$\frac{8}{125} + \frac{1}{100} - {(\frac{1}{2})}^{3}$

Step 1.7

Apply the product rule to $\frac{1}{2}$ .

$\frac{8}{125} + \frac{1}{100} - \frac{1^{3}}{2^{3}}$

Step 1.8

One to any power is one.

$\frac{8}{125} + \frac{1}{100} - \frac{1}{2^{3}}$

Step 1.9

Raise $2$ to the power of $3$ .

$\frac{8}{125} + \frac{1}{100} - \frac{1}{8}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{8}{125}$ by $\frac{8}{8}$ .

$\frac{8}{125} \cdot \frac{8}{8} + \frac{1}{100} - \frac{1}{8}$

Step 2.2

Multiply $\frac{8}{125}$ by $\frac{8}{8}$ .

$\frac{8 \cdot 8}{125 \cdot 8} + \frac{1}{100} - \frac{1}{8}$

Step 2.3

Multiply $\frac{1}{100}$ by $\frac{10}{10}$ .

$\frac{8 \cdot 8}{125 \cdot 8} + \frac{1}{100} \cdot \frac{10}{10} - \frac{1}{8}$

Step 2.4

Multiply $\frac{1}{100}$ by $\frac{10}{10}$ .

$\frac{8 \cdot 8}{125 \cdot 8} + \frac{10}{100 \cdot 10} - \frac{1}{8}$

Step 2.5

Multiply $\frac{1}{8}$ by $\frac{125}{125}$ .

$\frac{8 \cdot 8}{125 \cdot 8} + \frac{10}{100 \cdot 10} - (\frac{1}{8} \cdot \frac{125}{125})$

Step 2.6

Multiply $\frac{1}{8}$ by $\frac{125}{125}$ .

$\frac{8 \cdot 8}{125 \cdot 8} + \frac{10}{100 \cdot 10} - \frac{125}{8 \cdot 125}$

Step 2.7

Reorder the factors of $125 \cdot 8$ .

$\frac{8 \cdot 8}{8 \cdot 125} + \frac{10}{100 \cdot 10} - \frac{125}{8 \cdot 125}$

Step 2.8

Multiply $8$ by $125$ .

$\frac{8 \cdot 8}{1000} + \frac{10}{100 \cdot 10} - \frac{125}{8 \cdot 125}$

Step 2.9

Reorder the factors of $100 \cdot 10$ .

$\frac{8 \cdot 8}{1000} + \frac{10}{10 \cdot 100} - \frac{125}{8 \cdot 125}$

Step 2.10

Multiply $10$ by $100$ .

$\frac{8 \cdot 8}{1000} + \frac{10}{1000} - \frac{125}{8 \cdot 125}$

Step 2.11

Multiply $8$ by $125$ .

$\frac{8 \cdot 8}{1000} + \frac{10}{1000} - \frac{125}{1000}$

Step 3

Combine the numerators over the common denominator.

$\frac{8 \cdot 8 + 10 - 125}{1000}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $8$ by $8$ .

$\frac{64 + 10 - 125}{1000}$

Step 4.2

Add $64$ and $10$ .

$\frac{74 - 125}{1000}$

Step 4.3

Subtract $125$ from $74$ .

$\frac{- 51}{1000}$

Step 4.4

Move the negative in front of the fraction.

$- \frac{51}{1000}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{51}{1000}$

Decimal Form:

$- 0.051$