# How do you simplify #( \frac { \sqrt { 6} + \sqrt { 2} } { 4} ) ^ { 6} + ( \frac { \sqrt { 6} - \sqrt { 2} } { 4} ) ^ { 6}#?

##### 1 Answer

#### Explanation:

I'm going to do this in a tricky way, but I hope it will save us some work.

First, let's see if we can reduce the power of the first numerator by rewriting it as a NESTED radical.

Likewise, for the other numerator, we can write

Now we can substitute these expressions into the numerators and focus on simplifying

Now we can write out the binomial expansion of a cubed expression (much easier than writing out the expansion of something taken to the 6th power!)

Which simplifies to