Evaluate 3-(8*-1)÷3+(-9)^3

$3 - 8 \cdot - 1 \div 3 + {(- 9)}^{3}$

Step 1

Find the common denominator.

Write $3$ as a fraction with denominator $1$ .

$\frac{3}{1} - 8 \cdot - 1 \div 3 + {(- 9)}^{3}$

Multiply $\frac{3}{1}$ by $\frac{3}{3}$ .

$\frac{3}{1} \cdot \frac{3}{3} - 8 \cdot - 1 \div 3 + {(- 9)}^{3}$

Multiply $\frac{3}{1}$ by $\frac{3}{3}$ .

$\frac{3 \cdot 3}{3} - 8 \cdot - 1 \div 3 + {(- 9)}^{3}$

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

$\frac{3 \cdot 3}{3} - 8 \cdot - 1 \div 3 + \frac{{(- 9)}^{3}}{1}$

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

$\frac{3 \cdot 3}{3} - 8 \cdot - 1 \div 3 + \frac{{(- 9)}^{3}}{1} \cdot \frac{3}{3}$

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

$\frac{3 \cdot 3}{3} - 8 \cdot - 1 \div 3 + \frac{{(- 9)}^{3} \cdot 3}{3}$

Step 2

Combine the numerators over the common denominator.

$\frac{3 \cdot 3 - 8 \cdot - 1 + {(- 9)}^{3} \cdot 3}{3}$

Step 3

Simplify each term.

Multiply $3$ by $3$ .

$\frac{9 - 8 \cdot - 1 + {(- 9)}^{3} \cdot 3}{3}$

Multiply $- 8$ by $- 1$ .

$\frac{9 + 8 + {(- 9)}^{3} \cdot 3}{3}$

Raise $- 9$ to the power of $3$ .

$\frac{9 + 8 - 729 \cdot 3}{3}$

Multiply $- 729$ by $3$ .

$\frac{9 + 8 - 2187}{3}$

Step 4

Simplify the expression.

Add $9$ and $8$ .

$\frac{17 - 2187}{3}$

Subtract $2187$ from $17$ .

$\frac{- 2170}{3}$

Move the negative in front of the fraction.

$- \frac{2170}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{2170}{3}$

Decimal Form:

$- 723.\overline{3}$

Mixed Number Form:

$- 723 \frac{1}{3}$