# 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 \(a+b+c+d\)?