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AP EAMCET2014MathematicsTrigonometric Ratios & Identities

81^ - 63^ - 27^ + 9^ equals to

Options

  1. A6
  2. B0
  3. C2
  4. D4

Correct answer

D. 4

Step-by-step solution

aligned & 81^ - 63^ - 27^ + 9^ & = ( 81^ + 9^ )- [ (63^ )+ (27^ ) ] & = [ 81^ 81^ + 9^ 9^ ]- [ 63^ 63^ + 27^ 27^ ] & = [ 81^ 9^ + 9^ 81^ 9^ 81^ ] & - [ 63^ 27^ + 27^ 63^ 27^ 63^ ] & = [ (81^ +9^ ) ] 9^ (90^ -90^ ) & = [ (63^ +27^ ) ] 27^ (90^ -27^ ) & = 1 9^ 9^ 2 2 - 1 27^ 27^ 2 2 & = 2 27^ 27^ - 2 54^ aligned aligned & =2 [ 54^ - 18^ 18^ 54^ ] & =2 [ 2 36^ 18^ 18^ 36^ ] & =4 aligned

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