Evaluate ((3)^3)/3-9*3-(((1)^3)/3-9)

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

Step 1

Find the common denominator.

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

Multiply $- 9$ by $3$ .

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

Multiply $- 27$ by $3$ .

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

One to any power is one.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 9$ by $3$ .

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

Subtract $27$ from $1$ .

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

Cancel the common factor of $3$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Simplify the expression.

Subtract $81$ from $27$ .

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

Add $- 54$ and $26$ .

$\frac{- 28}{3}$

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:

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

Evaluate ((3)^3)/3-9*3-(((1)^3)/3-9)

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