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Omni-MATH / Alice is thinking of a positive real number x, and Bob is thinking of a positive real number y. Given that x^(√(y))=27 and (√(x))^(y)=9, compute xy.

Problem

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problem

Alice is thinking of a positive real number xx, and Bob is thinking of a positive real number yy. Given that xy=27x^{\sqrt{y}}=27 and (x)y=9(\sqrt{x})^{y}=9, compute xyx y.
Plain-text mathematical notation (without MathML)
Alice is thinking of a positive real number x, and Bob is thinking of a positive real number y. Given that x^(√(y))=27 and (√(x))^(y)=9, compute xy.
Original LaTeX notation
Alice is thinking of a positive real number $x$, and Bob is thinking of a positive real number $y$. Given that $x^{\sqrt{y}}=27$ and $(\sqrt{x})^{y}=9$, compute $x y$.

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Source and history

task_id
46e55f34-dde4-5125-abd9-67e3b3ad207b
task_key
test--46e55f34-dde4-5125-abd9-67e3b3ad207b
task_revision_id
1
config / split
/ test

Official source

initial import