Simplify $4^{2x}+4^x$

Question

How would one simplify the exponents of $4^{2x}+4^x$ (or if it is even possible)

I feel like there are some ways to simplify this using the exponent laws but I cannot find anything from it. Thanks!

Answer 1

$$4^{2x} +4^{x} =(4^{x})^2 +4^{x} =4^{x}( 4^{x} +1).$$

Answer 2

First of all, you will need to evaluate the power using $a^{mn}=(a^m)^n$: $$4^{2x}+4^x=(4^2)^x+4^x=16^x+4^x.$$ After you have done with evaluation of the power, you’ll continue with factoring out $4^x$ from the expression which will be your answer: $$4^x(4^x+1).$$