CPM Homework Help : CCA2 Problem 3-7

Bonnie and Dylan were both working on simplifying the expression at right. Each of their first steps is shown below.

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

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

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

Each of them is convinced that they have 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?

Hint:

There are multiple ways to simplify these expression.

Answer:

Both are correct.
Explain why this is possible.