Given the numbers

MATHEMATICS · Multi-part · CBSE · Mathematics · Number Systems · Number Systems

Problem

Given the numbers P=95/2,  Q=274/3,  R=37,  S=(13)−8P = 9^{5/2},\; Q = 27^{4/3},\; R = 3^{7},\; S = \left(\dfrac{1}{3}\right)^{-8}, answer the following questions. (i) Rewrite each of P, Q, R, SP,\, Q,\, R,\, S in the form 3k3^{k}, where kk is an integer. (ii) Arrange the numbers in descending order, clearly justifying each comparison. (iii) Which two of the numbers are closest in value? Explain your reasoning without using a calculator.

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