If $$a^{2x}=b, b^{2y}=c, c^{2z}=a$$​ then the value of $$xyz$$​ is:

Correct option is D

Given :

​$$a^{2x }=$$​ b

​$$b^{2y} =$$​ c

​$$c^{2z}$$= a

Concept Used:

$$(x^a)^b = x^{ab}$$​​

Solution :

We have,

​$$a^{2x }=$$​ b ---- (1)

​$$b^{2y} =$$​ c ---- (2)

​$$c^{2z}$$​= a ---- (3)

Substituting (1) in (2),

​$$(a^{2x})^{2y}$$​= c

​$$a^{4xy }= c$$​ ---- (4)

Substituting (4) in (3),

​$$(a^{4xy})^{2z} = a$$​​

​$$a^{8xyz} = a^1$$​​

Comparing the powers of a,

8xyz = 1

xyz =$$\frac18$$​​