# Summing the alphabets !

Algebra Level 4

$\displaystyle \sqrt{\left(\frac{1}{\sqrt{27}}\right)^{2-\frac{ \log_{5}{13}}{2 \log_{5}{9}}}}$ Can be expressed as: $3^{\frac{a}{b}} \times 13^{\frac{c}{d}}$ Where $$a$$ is a negative integer and $$b,c,d$$ are positive integers with $$\gcd(-a,b)=\gcd (c,d)=1$$. What is $$a+b+c+d$$?

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