Answer

 

is larger.

 

Answers will vary.

 

This can be shown by looking at the two numbers using the following:

·    multiplying powers with like bases

 

·    product of powers property

 

Example:                                     

                   

 

 

 

 

214 

 

1002

 

 

 

 

 

 

 

 

 

 

 

 

 

(27)2

 

(102)2 

 

 

 

 

 

 

 

 

both are squares - now look at the bases and compare

27

 

102

 

 

 

 

 

 

 

 

 

27

 

(2∙5)2

 

 

 

 

 

 

 

 

 

 

 

 

 

22∙25

 

22∙52

 

 

 

 

 

     

22  is found in both expressions and cancels out 

25

 

52

 

 

 

 

 

 

 

 

 

    32

25

 

 

 

 

 

 

 

 

Therefore:

214

1002