### Home > AC > Chapter 13 > Lesson 13.RE1-S > Problem2-124

2-124.

Donnie and Dylan were both working on simplifying the expression at right. The first step of each of their work is shown below.

$( \frac { 2 x ^ { 5 } y ^ { 4 } } { 8 x y ^ { 3 } } ) ^ { 3 }$

Donnie:     $\frac { 8 x ^ { 15 } y ^ { 12 } } { 512 x ^ { 3 } y ^ { 9 } }$

Dylan:     $( \frac { x ^ { 4 } y } { 4 } ) ^ { 3 }$

Each of them is convinced that he has started the problem correctly. Has either of them made an error? If so, explain the error completely. If not, explain how they can both be correct and verify that they will get the same, correct solution. Which student's method do you prefer? Why?

There are multiple ways to simplify this expression.

Both are correct.
Explain why this is possible.