If $x^{y}=64$ and x and y are positive integers, then $x + y$ can take how many values

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What this question tests

Your grasp of exponent rules — multiplying and dividing powers, power-of-a-power, and negative/zero exponents.

Adding exponents when multiplying bases that have the same exponent, or confusing (x^a)^b with x^(a·b).

If xy=64x^{y}=64xy=64 and x and y are positive integers, then x+yx + yx+y can take how many values