The value of m such that (2/9)³ x (4/81)-6 :

The value of m such that (2/9)³ x (4/81)-6 = (2/9)2m 1 is
(a) – 6
(b) 0
(c) – 4
(d) 3

Anurag Mishra Professor Asked on 23rd February 2016 in Maths.
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  • 1 Answer(s)

    Answer: (c) -4

    Solution:-
    (2/9)^3  x (4/81)^-6 = (2/9)^2m – 1
    (2/9)^3 x (2/9)^2 x (-6) =  (2/9)^2m – 1
    (2/9)^3 x (2/9)^-12 = (2/9)^2m – 1
    (2/9)^ 3 – 12 =  (2/9)^2m – 1
    (2/9)^-9 =  (2/9)^2m – 1
    Comparing on both side,
    – 9 = 2 m – 1
    2 m = – 9 + 1
    2 m = – 8
    m = -8/2
    m = -4

    Then, the value of m is -4.

    Hence, the correct answer is option (c) -4.

    Anurag Mishra Professor Answered on 25th February 2016.
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