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Maths-

General

Easy

Question

If A = $open square brackets table row 1 1 row 1 1 end table close square brackets$ and n $element of$ N, then Aⁿ is equal to-

2ⁿA
2^n–1 A
nA
None of these

The correct answer is: 2^n–1 A

we are given that A = $open square brackets table row 1 1 row 1 1 end table close square brackets$ and n $element of$ N and we need to find what An is equal to
$A equals open square brackets table row 1 1 row 1 1 end table close square brackets A squared space equals open square brackets table row 1 1 row 1 1 end table close square brackets open square brackets table row 1 1 row 1 1 end table close square brackets equals open square brackets table row 2 2 row 2 2 end table close square brackets equals 2 A space A cubed space equals A squared space space. A equals 2 A. A equals 2 left parenthesis A squared right parenthesis equals 2.2 A equals 2 to the power of left parenthesis 3 minus 1 right parenthesis end exponent space A space T h e n space i n space g e n e r a l space A space space n space space equals 2 to the power of n minus 1 end exponent A$

Therefore the correct option in choice 2

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