Determine which number is larger

Question

this is the problem: 

Using exponent rules; determine which number is largest 

 

2^75 and 3^50

Answer 1

This is a little tricky.

Rewrite 2⁷⁵ = 2^3*25 = (2³)²⁵ = 8²⁵ 

rewrite 3⁵⁰ = 3^2*25 = (3²)²⁵ = 9²⁵

 

Since they have the same exponent now, the one with the larger base will be bigger. So 3⁵⁰ is larger.

 

Hope this helped