Which two numbers (not digits) and two signs need to be interchanged to make the given equation correct?
$$14 + 7 \div 729 \times 81 - 9 = 500$$

Option (a) 81 and 9, $$\div$$ and $$\times$$

$$14 + 7 \times 729 \div 9 - 81 = 500$$

$$14+7\times81-81=500$$

$$14+567-81=500$$

500 = 500

The above-given equation is satisfied. So this is the correct answer.

Option (b) 14 and 9, - and $$\times$$

$$9 + 7 \div 729 - 81 \times 14 = 500$$

$$9+7\div729-81\times14=500$$

Option (c) 7 and 729, + and -

$$14 - 729 \div 7 \times 81 + 9 = 500$$

The above-given equation is not satisfied. Because it will give values in fractions. So this is not the correct answer.

Option (d) 81 and 7, + and $$\times$$

$$14 \times 81 \div 729 + 7 - 9 = 500$$

The above-given equation is not satisfied. Because it will give values in fractions. So this is not the correct answer.