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Question

Which of the following is equal to 8342?

A
2
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B
23
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C
24
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D
25
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Solution

The correct option is D 25
Need to simplify:–––––––––––––––––––8342

In the given exponent 8342, neither bases (8,4) nor exponents (3,2) are equal.

Let's try to make bases equal.
8342
=(23)3(22)2 [ As 8=2×2×2=23 and 4=2×2=22 ]

=23×322×2
[ <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Repeated exponentiation: (am)n=am×n ]

=2924

=294=25
[ <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Division rule of exponents: aman=amn]

8342=25–––––––

Therefore, option (d.) is the correct one.

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