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MATH / If 3^(x+y)=81 and 81^(x−y)=3, then what is the value of the product xy? Express your answer as a common fraction.

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problem

If 3x+y=813^{x + y} = 81 and 81x−y=3,81^{x - y} = 3, then what is the value of the product xyxy? Express your answer as a common fraction.
Plain-text mathematical notation (without MathML)
If 3^(x+y)=81 and 81^(x−y)=3, then what is the value of the product xy? Express your answer as a common fraction.
Original LaTeX notation
If $3^{x + y} = 81$ and $81^{x - y} = 3,$ then what is the value of the product $xy$? Express your answer as a common fraction.

level

Level 5

type

Algebra

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