Question

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

• A. $\frac{1}{4}$
• B. $\frac{1}{6}$
• C. $\frac{1}{8}$
• D. $\frac{1}{10}$

Answer 1

The correct option is C $\frac{1}{8}$

Given $a=b^{2x}$ (1)
$b=c^{2y}$ (2)
$c=a^{2x}$ (3)
Substituting the value of b from (2) in (1), we get
$a=(c^{2y}{)}^{2x}=c^{4xy}$ (4)
Substituting the value of c from (3) in (4), we get
$a=(a^{2z}{)}^{4xy}=a^{8xyz}$
or $a^1=a^{8xyz}⟹xyz=\frac{1}{8}$