# 2^(2x+y) = (4^x)(2^y)?

Is 22x+y = 4x2y? If I substitute various digits into the x and y variables, it works, but I can't understand why. Can anyone please explain this to me?

For example, if we choose x=3 and y=1,
2(2)(3)+1 = 27 = 128
2(2)(3)+1 = 4321 = 64(2) = 128

Thanks

## Answers and Replies

Integral
Staff Emeritus
Science Advisor
Gold Member
It follows from the basic rules of combining exponents.

$$x^a x^b = x^{(a+b)}$$

$$x^{ab} = (x^a)^b$$

I can't believe I didn't figure that out. Thank you!