MATHEMATICS · Multi-part · CBSE · Mathematics · Number Systems · Number Systems
Problem
Without using a calculator, compare the magnitudes of the following three numbers and arrange them in descending order:
123,312,223.
(i) Express each number in a form that involves either a common base or a common exponent, showing every intermediate step clearly.
(ii) Using the rewritten forms, order the numbers from the greatest to the least, providing full justification for each step of your comparison.
(iii) Comment on whether raising all three numbers to the same positive integer power would change their relative order, backing your statement with an explanation.