Evaluate (20^2)÷(3(5-9)^2+2)

$20^{2} \div (3 {(5 - 9)}^{2} + 2)$

Rewrite the division as a fraction.

$\frac{20^{2}}{3 {(5 - 9)}^{2} + 2}$

Raise $20$ to the power of $2$ .

$\frac{400}{3 {(5 - 9)}^{2} + 2}$

Simplify the denominator.

Subtract $9$ from $5$ .

$\frac{400}{3 {(- 4)}^{2} + 2}$

Raise $- 4$ to the power of $2$ .

$\frac{400}{3 \cdot 16 + 2}$

Multiply $3$ by $16$ .

$\frac{400}{48 + 2}$

Add $48$ and $2$ .

$\frac{400}{50}$

$\frac{400}{50}$

Divide $400$ by $50$ .

$8$

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