Evaluate ((1-3)^2-14)/( square root of 16-20÷2+9)

$\frac{{(1 - 3)}^{2} - 14}{\sqrt{16} - 20 \div 2 + 9}$

Cancel the common factor of $20$ and $2$ .

Factor $2$ out of $20$ .

$\frac{{(1 - 3)}^{2} - 14}{\sqrt{16} - 2 \cdot 10 \div 2 + 9}$

Cancel the common factors.

Factor $2$ out of $2$ .

$\frac{{(1 - 3)}^{2} - 14}{\sqrt{16} - 2 \cdot 10 \div 2 (1) + 9}$

Cancel the common factor.

$\frac{{(1 - 3)}^{2} - 14}{\sqrt{16} - 2 \cdot 10 \div 2 \cdot 1 + 9}$

Rewrite the expression.

$\frac{{(1 - 3)}^{2} - 14}{\sqrt{16} - \frac{10}{1} + 9}$

Divide $10$ by $1$ .

$\frac{{(1 - 3)}^{2} - 14}{\sqrt{16} - 1 \cdot 10 + 9}$

Simplify the numerator.

Subtract $3$ from $1$ .

$\frac{{(- 2)}^{2} - 14}{\sqrt{16} - 1 \cdot 10 + 9}$

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

$\frac{4 - 14}{\sqrt{16} - 1 \cdot 10 + 9}$

Subtract $14$ from $4$ .

$\frac{- 10}{\sqrt{16} - 1 \cdot 10 + 9}$

Simplify the denominator.

Rewrite $16$ as $4^{2}$ .

$\frac{- 10}{\sqrt{4^{2}} - 1 \cdot 10 + 9}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{- 10}{4 - 1 \cdot 10 + 9}$

Multiply $- 1$ by $10$ .

$\frac{- 10}{4 - 10 + 9}$

Subtract $10$ from $4$ .

$\frac{- 10}{- 6 + 9}$

Add $- 6$ and $9$ .

$\frac{- 10}{3}$

Move the negative in front of the fraction.

$- \frac{10}{3}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{10}{3}$

Decimal Form:

$- 3.\overline{3}$

Mixed Number Form:

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