evaluate the sum

 Dear Student,

(i) ${\left(\frac{1}{3}\right)}^{-2}+ {\left(\frac{1}{4}\right)}^{-2}+ {\left(\frac{1}{6}\right)}^{-2}$
= 3^{2_​​​​} + 4² + 6^{2_{​​​​​​}}..........(as ${\left(\frac{1}{a}\right)}^{-b}$ = a^{​​​​​​b}​​​ )
= 9 + 16 + 36
= 61

(ii) 2^-7 $\times$ [(-2)^-3]^-4
= 2^-7 $\times$ (-2)¹².............(as ((a)^b​​​​​​)^c​​​​​ = a^​​bc )
= 2^-7 $\times$ 2¹²............( as (-a)^b​​​​​​ = a^{​​​​​​b}​​​ if b is even number )
= 2^(-7+12)...........( as a^{​​​​​​b}​​​​​$\times$ a^​​​c = a^{​​​​​​b+c} )