Basic Math Examples

$\frac{1}{8} + {(\frac{1}{8})}^{2} - \frac{5}{512}$

Step 1

Find the common denominator.

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Step 1.1

Multiply $\frac{1}{8}$ by $\frac{64}{64}$ .

$\frac{1}{8} \cdot \frac{64}{64} + {(\frac{1}{8})}^{2} - \frac{5}{512}$

Step 1.2

Multiply $\frac{1}{8}$ by $\frac{64}{64}$ .

$\frac{64}{8 \cdot 64} + {(\frac{1}{8})}^{2} - \frac{5}{512}$

Step 1.3

Write ${(\frac{1}{8})}^{2}$ as a fraction with denominator $1$ .

$\frac{64}{8 \cdot 64} + \frac{{(\frac{1}{8})}^{2}}{1} - \frac{5}{512}$

Step 1.4

Multiply $\frac{{(\frac{1}{8})}^{2}}{1}$ by $\frac{512}{512}$ .

$\frac{64}{8 \cdot 64} + \frac{{(\frac{1}{8})}^{2}}{1} \cdot \frac{512}{512} - \frac{5}{512}$

Step 1.5

Multiply $\frac{{(\frac{1}{8})}^{2}}{1}$ by $\frac{512}{512}$ .

$\frac{64}{8 \cdot 64} + \frac{{(\frac{1}{8})}^{2} \cdot 512}{512} - \frac{5}{512}$

Step 1.6

Multiply $8$ by $64$ .

$\frac{64}{512} + \frac{{(\frac{1}{8})}^{2} \cdot 512}{512} - \frac{5}{512}$

Step 2

Combine the numerators over the common denominator.

$\frac{64 + {(\frac{1}{8})}^{2} \cdot 512 - 5}{512}$

Step 3

Simplify each term.

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Step 3.1

Apply the product rule to $\frac{1}{8}$ .

$\frac{64 + \frac{1^{2}}{8^{2}} \cdot 512 - 5}{512}$

Step 3.2

One to any power is one.

$\frac{64 + \frac{1}{8^{2}} \cdot 512 - 5}{512}$

Step 3.3

Raise $8$ to the power of $2$ .

$\frac{64 + \frac{1}{64} \cdot 512 - 5}{512}$

Step 3.4

Cancel the common factor of $64$ .

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Step 3.4.1

Factor $64$ out of $512$ .

$\frac{64 + \frac{1}{64} \cdot (64 (8)) - 5}{512}$

Step 3.4.2

Cancel the common factor.

$\frac{64 + \frac{1}{64} \cdot (64 \cdot 8) - 5}{512}$

Step 3.4.3

Rewrite the expression.

$\frac{64 + 8 - 5}{512}$

Step 4

Simplify by adding and subtracting.

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Step 4.1

Add $64$ and $8$ .

$\frac{72 - 5}{512}$

Step 4.2

Subtract $5$ from $72$ .

$\frac{67}{512}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{67}{512}$

Decimal Form:

$0.13085937 \dots$