# The Magnificent Operator

Let me define an operator for two natural numbers $$a,b$$ as $$[[]a,b[]]$$

$$[[]a,b[]]=\frac{a^b}{b^a}\frac{b^b}{a^a}$$

Now, if $$a+b\leq15$$, with $$b\geq8$$, find the number of ordered pairs $$(a,b)$$ for which $$[[]a,b[]]$$ is a perfect square of an integer.

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