Simplify the given expression.

\(\frac{13 \div\{6-6 \div(7-9) \times 8+9\}}{5+5 \times 5 \div 5 \text { of } 5}\)

Given:

Formula used:

Order of operations (BODMAS/BIDMAS): Brackets, Orders (i.e., powers and square roots, etc.), Division and Multiplication, Addition and Subtraction

Calculation:

\(\dfrac{13 ÷{6-6 ÷(7-9) × 8+9}}{5+5 × 5 ÷ 5 \text { of } 5}\)

First, solve the inner bracket: (7-9)

⇒ (7-9) = -2

Next, solve the division inside the inner bracket: 6 ÷ -2

⇒ 6 ÷ -2 = -3

Now, multiply by 8: -3 × 8

⇒ -3 × 8 = -24

Now, solve the expression inside the outer bracket: 6 - (-24) + 9

⇒ 6 - (-24) + 9 = 6 + 24 + 9

⇒ 6 + 24 + 9 = 39

Now, divide 13 by 39:

⇒ 13 ÷ 39 =\( \dfrac{1}{3}\)

Next, solve the denominator: 5 + 5 × 5 ÷ 5 of 5

First, solve the 'of' operation: 5 of 5

⇒ 5 of 5 = 25

Next, solve the multiplication and division: 5 × 5 ÷ 25

⇒ 5 × 5 = 25

⇒ 25 ÷ 25 = 1

Now, add 5: 5 + 1

⇒ 5 + 1 = 6

Finally, combine the numerator and denominator:

⇒ \(\dfrac{1}{3} ÷ 6\)

⇒ \(\dfrac{1}{3} × \dfrac{1}{6}\)

⇒ \(\dfrac{1}{18}\)

∴ The correct answer is option (1).