Let . Answer the…

MATHEMATICS · Multi-part · AoPS · Mathematics · Follow the Rules · Follow the Rules

Problem

Let

C = \dfrac{12^{3}\times 6^{-2}\times 18^{4}}{3^{-5}\times 36^{3}}

. Answer the following: (i) Express every number in

C

as a product of powers of the prime bases

2

and

3

, and rewrite

C

accordingly. (ii) Simplify separately for the bases

2

and

3

to reduce

C

to the form

2^{m}\,3^{n}

, where

m

and

n

are integers. (iii) Calculate the numerical value of

C