Summing the alphabets !

Algebra Level 4

(127)2log5132log59\displaystyle \sqrt{\left(\frac{1}{\sqrt{27}}\right)^{2-\frac{ \log_{5}{13}}{2 \log_{5}{9}}}} Can be expressed as: 3ab×13cd3^{\frac{a}{b}} \times 13^{\frac{c}{d}} Where aa is a negative integer and b,c,db,c,d are positive integers with gcd(a,b)=gcd(c,d)=1\gcd(-a,b)=\gcd (c,d)=1. What is a+b+c+da+b+c+d?

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