# 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

**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.