Rewrite in simplest rational exponent form √x • 4√x. show each step of your process.

I like to think of radicals (or square roots) just as x terms-
here, we have the equivalent (kind of) to x * 4x. 
Since these are both x terms and 4x= x*x*x*x, we can simply write 5x.

Im not sure what your teacher is asking you to communicate, but most simply would like to see evidence that you understand the material rather than simply looking up the answer... (i mean without reading an explanation xD)
4√x= √x*√x*√x*√xso √x • 4√x =5√x