Question

Find the value of ${25}^{-2{\log }_{5}3}$

Answer 1

${25}^{-2{\log }_{5}3}={\left(5^2\right)}^{-2{\log }_{5}3}=5^{-4{\log }_{5}3}$ $[\because n{\log }_{a}M={\log }_a{M}^n]$
$=5^{{\log }_5{3}^{-4}}=3^{-4}=\frac{1}{3^4}=\frac{1}{81}$ $[\because b^{{\log }_{b}a}=a]$