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UKMT Senior Mathematical Challenge, 2020

Algebra Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The real numbers $x$ and $y$ satisfy the equations $4^y = \dfrac{1}{8(\sqrt{2})^{x+2}}$ and $9^x \times 3^y = 3\sqrt{3}$ . What is the value of $5^{x+y}$ ?

(A) $5\sqrt{5}$ (B) $5$ (C) $\sqrt{5}$ (D) $\dfrac{1}{5}$ (E) $\dfrac{1}{\sqrt{5}}$

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