\(\underbrace{a+a+a+\cdots+a}_{n\ \text{times}}=a^2b\) and…

GATE · 2018 · CE · Set 2 · General Aptitude

a+a+a+⋯+a⏟n times=a2b\underbrace{a+a+a+\cdots+a}_{n\ \text{times}}=a^2b and b+b+b+⋯+b⏟m times=ab2\underbrace{b+b+b+\cdots+b}_{m\ \text{times}}=ab^2, 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)\left(\underbrace{m+m+m+\cdots+m}_{n\ \text{times}}\right)\left(\underbrace{n+n+n+\cdots+n}_{m\ \text{times}}\right)?

  1. A.

    2a2b2

  2. B.

    a4b4

  3. C.

    ab(a + b)

  4. D.

    a2 + b2

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