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Question

Choose the correct expression(s).

A
5202552021=54
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B
52021102021=(12)2021
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C
25101162022=(56)2022
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Solution

The correct option is C 25101162022=(56)2022
Let's check all the given expressions one-by-one:

5202552021

=520252021=54
[ <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Division rule of exponents: aman=amn ]

52021102021

=(510)2021=(12)2021
[ <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Division rule of exponents: anbn=(ab)n ]

25101162022
Here, neither bases nor exponents are same. Division rule of exponents can not be applied directly.

Let's try to make exponents same.

25101162022
=(52)101162022
(25=5×5=52)

=52×101162022
[ <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Repeated exponentiation: (am)n=am×n ]

=5202262022

25101162022=(56)2022
[ <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Division rule of exponents: anbn=(ab)n ]

Therefore, all the given expressions are correct.

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