Question

write in ascending order

2^60,3^48,4^36,5^24

Answer 1

When ever you find number with huge distinct powers it is always suggested to bring it under a single power and comparing the bases rather than bringing it to single base.

Take the powers of the numbers 60,48,36,24

GCD of 60,48,36,24 is 12. Now separate the power 12 and compare the numbers i.e.,

2^60 = (2^5)^12 = 32^12 (Since, 60 = 12*5 and a^(b*c)=(a^b)^c)

3^48 = (3^4)^12 = 81^12

4^36 = (4^3)^12 = 64^12

5^24 = (5^2)^12 = 25^12

Now all the powers are same and we can compare the bases and we can arrange them in ascending order as follows

5^24 < 2^60 < 4^36 < 3^48

This approach helps in comparing any number of bases with large powers.