GregMat Solve Quant Problems - Please Help

[hijuwonim]

Hi,
In this question’s solution video, Greg says “if you raise both of these to the one over fifty power, you get three to the power of fifteen and five to the power of eight”. Could anyone please help me understand what it means by “if you raise both of these to one over fifty power”?

3^750 = 3^(5015)
5^400 = 5^(508)
We know that 3^50 is smaller than 5^50, so how can we be sure that an additional 3^15 is going to make the 3^(5015) larger than 5^(50*8)?

(Greg mentions that the GRE calculator can compare 3^15 and 5^8, but let’s say that we’re not using the calculator for now.)

[prakithgre]

It would be better if u visualise it in the form of a graph that would give you a better insight n^m is an exponential curve. Try for a smaller set it’ll be much easier to understand for example 5^10 and 3^20 or something.