Identify the number that will replace the question mark in the second equation based on the relationship represented in the first equation.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 456
The first equation shows the rule: each number is raised to a power that is one more than the number of squares drawn round it.
a sits in 1 square, so it is squared: \(a^2\)
b sits in 2 squares, so it is cubed: \(b^3\)
c sits in 3 squares, so its power is 4: \(c^4\)
In the second figure:
7 sits in 2 squares: \(7^3=343\)
2 sits in 4 squares: \(2^5=32\)
3 sits in 3 squares: \(3^4=81\)
Sum \(=343+32+81=456\)