Question

  9¹⁶.3¹⁷

27¹¹.81⁵

Answer 1

\(\frac{9^{16}\cdot3^{17}}{27^{11}\cdot81^5}=\frac{3^{32}.3^{17}}{3^{33}.3^{20}}=\frac{3^{49}}{3^{53}}=\frac{1}{3^4}=\frac{1}{81}\)

Answer 2

9¹⁶.3¹⁷ = (3²)¹⁶.3¹⁷ = 3³².3¹⁷ = 3⁴⁹

27¹¹.81⁵ = (3³)¹¹.(3⁴)⁵ = 3³³.3²⁰ = 3⁵³

Answer 3

\(\frac{9^{16}.3^{17}}{27^{11}.81^5}=\frac{\left(3^2\right)^{16}.3^{17}}{\left(3^3\right)^{11}.\left(3^4\right)^5}=\frac{3^{32}.3^{17}}{3^{33}.3^{20}}=\frac{3^{32+17}}{3^{33+20}}=\frac{3^{49}}{3^{53}}=3^{-4}\)