Understanding the Exponential Equation 2^(2x+y) = (4^x)(2^y)

[PsychStudent]

Is 2^2x+y = 4^x2^y? 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

 

[Integral]

It follows from the basic rules of combining exponents.

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

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

 

[PsychStudent]

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