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How many digits are in the value of the following expression: \(2^{2001}\times 5^{1950}\div 4^{27}\)?

 Mar 12, 2018
 #1
avatar+98130 
+1

2^2001 * 5^1950

______________  =

     4^27

 

2^2001 * 5^1950

_____________    =

        (2^2)^27

 

2^2001 * 5^1950

_____________    =

       2^54

 

2^1947 * 5^1950 =

 

2^ 1947 * 5^1947 * 5^3  =

 

(2*5)^1947  * 5^3  =

 

10^1947 * 125  =

 

125 x 10^1947 =

 

1.25 x 10^1949

 

So...... 1950 digits

 

 

cool cool cool

 Mar 12, 2018
 #2
avatar+809 
+1

Thank you so much, CPhill! Wow, amazing! I understand it much better now!

mathtoo  Mar 12, 2018

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