### Home > AC > Chapter 14 > Lesson 14.3.1.2 > Problem 3-30

3-30.

Derek and Donovan were trying to solve the equation 4

^{4}= 16. Derek had an idea.^{x}

*“I know,”*he said.*“Isn't*16*equal to*4^{2}*?”*

*“Yeah, so what?”*said Donovan.

*“That means that we can rewrite the equation to look like*4^{4}= (4^{2})replied Derek.^{x}. This is much easier to solve!”

*“Yes,”*said Donovan.*“That makes sense. Isn't there another way, too? Since*4*is the same as*2^{2}*and*16*is the same as*2^{4}*,*(2

can't we rewrite it as^{2})^{4}= (2^{4})Homework Help ✎^{x}?”What do you think of Derek's and Donovan's methods? Will they both work?

Use both methods to solve 4

^{4}= 16^{x}Now solve 3

^{5}= 9^{2}^{x}^{ }.

Are these methods violating any rules or properties of exponents?

*x* = 2

*x* = 1.25