Simplifying large Powers of 2 - My Favorite Problems Ep. 8

Simplifying the fraction 2^2014 - 2^2013 / 2^2013 - 2^2012 without a calculator.

Solve without a calculator: 2^2014 - 2^2013 / 2^2013 - 2^2012

Math Kangaroo math problem, high school. Factoring large exponents.

[Mine_Is]

Bro don't give up! I will be with you

[YTmc]

Decent solution, but kind of inelegant.

I prefer noticing that 2^x - 2^(x-1) = 2^(x-1) (e.g. 8-4=4, 1024-512=512)
Applying that to the top and bottom we get (2^2013)/(2^2012).
And then by laws of exponents, we get 2^1, and finally 2.

[RyanLewis-Johnson-wqxs]

I got the answer right in 0.3 recurring seconds no time to look it up.

[Mine_Is]

I do first comment in this amazing video😎