Evaluate (-12)÷((-3+16÷8)^3)+2

$(- 12) \div {(- 3 + 16 \div 8)}^{3} + 2$

Step 1

Simplify each term.

Rewrite the division as a fraction.

$\frac{- 12}{{(- 3 + 16 \div 8)}^{3}} + 2$

Cancel the common factor of $16$ and $8$ .

Factor $8$ out of $16$ .

$\frac{- 12}{{(- 3 + 8 \cdot 2 \div 8)}^{3}} + 2$

Cancel the common factors.

Factor $8$ out of $8$ .

$\frac{- 12}{{(- 3 + 8 \cdot 2 \div 8 (1))}^{3}} + 2$

Cancel the common factor.

$\frac{- 12}{{(- 3 + 8 \cdot 2 \div 8 \cdot 1)}^{3}} + 2$

Rewrite the expression.

$\frac{- 12}{{(- 3 + \frac{2}{1})}^{3}} + 2$

Divide $2$ by $1$ .

$\frac{- 12}{{(- 3 + 2)}^{3}} + 2$

Simplify the denominator.

Add $- 3$ and $2$ .

$\frac{- 12}{{(- 1)}^{3}} + 2$

Raise $- 1$ to the power of $3$ .

$\frac{- 12}{- 1} + 2$

Divide $- 12$ by $- 1$ .

$12 + 2$

Step 2

Add $12$ and $2$ .

$14$