Useful property: \((xy)^n = (x^n)(y^n)\)

QUANTITY A: \(3^{40}+3^{40}+3^{40}\)
In the same way that k + k + k = 3k, we can also say that \(3^{40}+3^{40}+3^{40}=3(3^{40})\)

QUANTITY B: \(6^{40}\)
We can rewrite 6 as follows: \((2 \times 3)^{40}\)
Then we can apply the above property to get: \((2^{40})(3^{40})\)


So we now have:
QUANTITY A: \(3(3^{40})\)
QUANTITY B: \((2^{40})(3^{40})\)

At this point, we can divide both quantities by \(3^{40}\) to get:
QUANTITY A: \(3\)
QUANTITY B: \(2^{40}\)

At this point it is clear that, Quantity B is greater.

Answer: B

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