# If 27x =9/3x, then what is the value of 1/x4?

If 27^{x} =9/3^{x}, then what is the value of 1/x^{4}?

- 4
- 10
- 8
- 16

**Answer: (4) 16**

**Explanation:-
27 ^{x} = 9/3^{x}
3^{x} x 3^{3x} = 3^{2}
3^{(x + 3x)} = 3^{2}
**Comparing on both side,

x + 3x = 2

4x = 2

x = 2/4

x = 1/2

The value of 1/x^{4} = 1/(1/2)^{4}

= (2)^{4} = 2 x 2 x 2 x 2

= 16

Then, the value of 1/x^{4} is 16.

Hence, the answer is (4) 16.