To simplify this expression, we first use the properties of logarithms:

log_a^n = n*log_a(b)

So, we can rewrite the expression as:

log2^6 + log2^3 - log2^9 = 6log2(2) + 3log2(2) - 9*log2(2)

Now, we simplify by evaluating the logarithms:

6log2(2) = 6
3log2(2) = 3
9*log2(2) = 9

Now, substitute these values back into the expression:

6 + 3 - 9 = 0

Therefore, log2^6 + log2^3 - log2^9 simplifies to 0.