SOLUTION: Find the number of digits of expression in 6^3�4^11�5^5.

Question 980298: Find the number of digits of expression in 6^3�4^11�5^5.
Answer by onlinepsa(22) (Show Source): You can put this solution on YOUR website!
Find the number of digits of expression in 6^3�4^11�5^5.
6^3 � 4^11 � 5^5

=2^3 x 3^3 � 2^22 �5^5.

= 2^25 x 3^3 x 5^5

= 2^20 x 3^3 x (5^5 x 2^25)

= 2^20 x 3^3 x [100,000]

= 2^20 x 27 x [100,000]

= (2^10)^2 x 27 x [100,000]

= (1024)^2 x 27 x [100,000]

To find the number of digits of 1024^2, we can take a lower value below 1024 and a higher one to see what the behaviour is:

(1000)^2 = 1000*1000 = 1,000,000 [7 digits]
(2000)^2 = 2000*2000 = 4,000,000 [7 digits]
In any case the number of digits remain same.
To, find the number of digits we can take 1000 in place of 1024;

(1024)^2 x 27 x [100,000]
= (1000)^2 x 27 x [100,000]
=2,700,000,000,000

Number of digits = 13.

Thanks,
PRD
https://onlinepsa.wordpress.com
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