Answer: one.
Explanation:
Let's break down the numerator first.
That ugly mess can be re-written as:
2^(2x+2y) times 2^(2y+2z) times 2^(2z+2x). Recall that (a^b)+(a^c)=a^(b+c).
2^(2x+2y) times 2^(2y+2z) times 2^(2z+2x) equals 2^(4x+4y+4z).
Let's break down the denominator now.
That mess can be re-written as:
2^x times 2^y times 2^z.
That can be re-written as 2^(x+y+z).
2^(x+y+z) all to the 4th power equals 2^(4x+4y+4z).
The denominator and numerator equal one another.
Bam.
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