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If p=3^ 1 3 3^ 2 9 3^ 3 27 , then p^ 4 3 =

Options

  1. A3^ 1 4
  2. B3
  3. C9
  4. D3^ 3 4

Correct answer

B. 3

Step-by-step solution

We have, p=3^ 1 3 3^ 2 9 3^ 3 27 =3^ 1 3 [1+ 2 3 + 3 9 + . ] =3^ 1 3 [ a 1-r + a r (1-r)² ] aligned & 1 3 [ 1 1- 1 3 + 1 1 3 (1- 1 3 )² ] =& 3 aligned =3^ 1 3 [ 3 2 + 3 4 ] =3^ 1 3 [ 12+6 8 ] =3^ 1 3 ( 18 8 ) =3^ 3 4 Now, p^ 4 / 3 = (3^ 3 4 )^ 4 3 =3^ 3 4 4 3 =3¹=3

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