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a + a + a +... + a (n times) = a² b and b + b + b +... + b (m times) = ab², where a, b, n and m are natural numbers. What is the value of (m + m + m +... + m (n times))(n + n + n +... + n (m times))?

1. 2a²b²
2. a⁴b⁴
3. ab(a + b)
4. a² + b²

Correct answer: a⁴b⁴

Solution

The expressions given simplify to a²b and ab², respectively. When calculating (m times b) and (n times a), we find that multiplying these results leads to a⁴b⁴, as each term contributes to the overall exponentiation of a and b.

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