Mathematics

Problem

Given the numbers

P = 9^{5/2},\; Q = 27^{4/3},\; R = 3^{7},\; S = \left(\dfrac{1}{3}\right)^{-8}

, answer the following questions. a. (i) Rewrite each of

P,\, Q,\, R,\, S

in the form

3^{k}

, where

k

is an integer. b. (ii) Arrange the numbers in descending order, clearly justifying each comparison. c. (iii) Which two of the numbers are closest in value? Explain your reasoning without using a calculator.

Browse the problem library