How to evaluate exponential logarithmic expression with decimal bases and infinite GP sums

Let $\alpha = \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \ldots \infty$ and
$\beta = \frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \ldots \infty$. Then the value of
$(0.2)^{\log_{\sqrt{5}}(\alpha )} + (0.04)^{\log_{5}(\beta )}$ is equal to :

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