Basic Math Examples

$\frac{{(3)}^{3}}{3} - 9 \cdot 3 - (\frac{{(1)}^{3}}{3} - 9)$

Step 1

Find the common denominator.

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Step 1.1

Write $- 9 \cdot 3$ as a fraction with denominator $1$ .

$\frac{{(3)}^{3}}{3} + \frac{- 9 \cdot 3}{1} - (\frac{{(1)}^{3}}{3} - 9)$

Step 1.2

Multiply $\frac{- 9 \cdot 3}{1}$ by $\frac{3}{3}$ .

$\frac{{(3)}^{3}}{3} + \frac{- 9 \cdot 3}{1} \cdot \frac{3}{3} - (\frac{{(1)}^{3}}{3} - 9)$

Step 1.3

Multiply $\frac{- 9 \cdot 3}{1}$ by $\frac{3}{3}$ .

$\frac{{(3)}^{3}}{3} + \frac{- 9 \cdot 3 \cdot 3}{3} - (\frac{{(1)}^{3}}{3} - 9)$

Step 1.4

Write $- (\frac{{(1)}^{3}}{3} - 9)$ as a fraction with denominator $1$ .

$\frac{{(3)}^{3}}{3} + \frac{- 9 \cdot 3 \cdot 3}{3} + \frac{- (\frac{{(1)}^{3}}{3} - 9)}{1}$

Step 1.5

Multiply $\frac{- (\frac{{(1)}^{3}}{3} - 9)}{1}$ by $\frac{3}{3}$ .

$\frac{{(3)}^{3}}{3} + \frac{- 9 \cdot 3 \cdot 3}{3} + \frac{- (\frac{{(1)}^{3}}{3} - 9)}{1} \cdot \frac{3}{3}$

Step 1.6

Multiply $\frac{- (\frac{{(1)}^{3}}{3} - 9)}{1}$ by $\frac{3}{3}$ .

$\frac{{(3)}^{3}}{3} + \frac{- 9 \cdot 3 \cdot 3}{3} + \frac{- (\frac{{(1)}^{3}}{3} - 9) \cdot 3}{3}$

Step 2

Combine the numerators over the common denominator.

$\frac{{(3)}^{3} - 9 \cdot 3 \cdot 3 - (\frac{{(1)}^{3}}{3} - 9) \cdot 3}{3}$

Step 3

Simplify each term.

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Step 3.1

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

$\frac{27 - 9 \cdot 3 \cdot 3 - (\frac{{(1)}^{3}}{3} - 9) \cdot 3}{3}$

Step 3.2

Multiply $- 9 \cdot 3 \cdot 3$ .

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Step 3.2.1

Multiply $- 9$ by $3$ .

$\frac{27 - 27 \cdot 3 - (\frac{{(1)}^{3}}{3} - 9) \cdot 3}{3}$

Step 3.2.2

Multiply $- 27$ by $3$ .

$\frac{27 - 81 - (\frac{{(1)}^{3}}{3} - 9) \cdot 3}{3}$

Step 3.3

One to any power is one.

$\frac{27 - 81 - (\frac{1}{3} - 9) \cdot 3}{3}$

Step 3.4

To write $- 9$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{27 - 81 - (\frac{1}{3} - 9 \cdot \frac{3}{3}) \cdot 3}{3}$

Step 3.5

Combine $- 9$ and $\frac{3}{3}$ .

$\frac{27 - 81 - (\frac{1}{3} + \frac{- 9 \cdot 3}{3}) \cdot 3}{3}$

Step 3.6

Combine the numerators over the common denominator.

$\frac{27 - 81 - \frac{1 - 9 \cdot 3}{3} \cdot 3}{3}$

Step 3.7

Simplify the numerator.

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Step 3.7.1

Multiply $- 9$ by $3$ .

$\frac{27 - 81 - \frac{1 - 27}{3} \cdot 3}{3}$

Step 3.7.2

Subtract $27$ from $1$ .

$\frac{27 - 81 - \frac{- 26}{3} \cdot 3}{3}$

Step 3.8

Cancel the common factor of $3$ .

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Step 3.8.1

Move the leading negative in $- \frac{- 26}{3}$ into the numerator.

$\frac{27 - 81 + \frac{26}{3} \cdot 3}{3}$

Step 3.8.2

Cancel the common factor.

$\frac{27 - 81 + \frac{26}{3} \cdot 3}{3}$

Step 3.8.3

Rewrite the expression.

$\frac{27 - 81 + 26}{3}$

Step 4

Simplify the expression.

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Step 4.1

Subtract $81$ from $27$ .

$\frac{- 54 + 26}{3}$

Step 4.2

Add $- 54$ and $26$ .

$\frac{- 28}{3}$

Step 4.3

Move the negative in front of the fraction.

$- \frac{28}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{28}{3}$

Decimal Form:

$- 9.\overline{3}$

Mixed Number Form:

$- 9 \frac{1}{3}$