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On simplification of $$\left[\frac{(1.331)^{-1} + (1.331)^{-2} + ... + (1.331)^{-6}}{(1.331)^{-2} + (1.331)^{-3} + ... + (1.331)^{-7}}\right]^{\frac{1}{3}}$$
Take $$1.331^{-1}$$ common from the denominator. As a result of which the numerator and denominator effectively cancel out. Hence the fraction effectivel becomes
$$\left(\frac{1}{1.331^{-1}}\right)^{\frac{1}{3}}$$
or $$\left(1.331^1\right)^{\frac{1}{3}}=1.331^{\frac{1}{3}}=1.1$$ which is the correct answer
