ExplanationIf x y = 64 and x and y are positive integers, perhaps the most obvious possibility is that x = 8 and y = 2. However, “all such values” implies that other solutions are

possible. One shortcut is noting that only an even base, when raised to a power, could equal 64. So you only have to worry about even possibilities for x. Here are all the possibilities:

\(2^6 = 64\) → \(x + y = 8\)

\(4^3 = 64\) → \(x + y = 7\)

\(8^2 = 64\) → \(x + y = 10\)

\(64^1 = 64\) → \(x + y = 65\)

The only possible values of x + y listed among the choices are 7, 8, and 10.

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Sandy

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