Mathematics

Problem

The integer

3600

is used in several measurement systems. Work through the steps below: a. (i) Write

3600

in its prime–factor form and hence express it as

2^a\, 3^b\, 5^c

, where

a

b

and

c

are non-negative integers. b. (ii) Using the result of part (i), determine integers

m

and

n

such that

3600 = 6^m\times 10^n

. c. (iii) Show that

3600

can also be written as a single power

60^p

and find the value of

p

. d. (iv) Compare the totals

a+b+c

m+n

and

p

. Which of the three representations uses the least total exponent? Give a brief reason for your answer.