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Omni-MATH / If a and b are positive real numbers such that a⋅2^(b)=8 and a^(b)=2, compute a^(log₂a)2^(b²).

Problem

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problem

If aa and bb are positive real numbers such that a⋅2b=8a \cdot 2^{b}=8 and ab=2a^{b}=2, compute alog2a2b2a^{\log _{2} a} 2^{b^{2}}.
Plain-text mathematical notation (without MathML)
If a and b are positive real numbers such that a⋅2^(b)=8 and a^(b)=2, compute a^(log₂a)2^(b²).
Original LaTeX notation
If $a$ and $b$ are positive real numbers such that $a \cdot 2^{b}=8$ and $a^{b}=2$, compute $a^{\log _{2} a} 2^{b^{2}}$.

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Source and history

task_id
5818e30e-3323-58b4-9d2c-e22233621450
task_key
test--5818e30e-3323-58b4-9d2c-e22233621450
task_revision_id
1
config / split
/ test

Official source

initial import