'99 ZX6R Carburation Question.

My '99 ZX6R runs great up to about 7 or 8k rpm's but after that the power seems kind of chocked down and the power comes on and off as if the engine is starving for fuel. I cleaned the air filter and the problem persists. I haven't changed spark plugs or cleaned out the carbs yet. I bought the bike last year with 9k miles on it so I'm thinking maybe it sat for awhile and the carbs got gummed up. I've put 7k miles on it so far though and the problem hasn't gotten any better or worse. Any ideas?



P.S. It seems to be the 49 state model. I'm in California but it doesn't have the CA equipment on it.