Question

If $a^x=\sqrt{b},b^y=\sqrt[3]{3c}$ and $c^z=\sqrt{a}$ then the value of $xyz$

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{6}$
• D. $\frac{1}{12}$

Answer 1

The correct option is D $\frac{1}{12}$

$a^x=\sqrt{b}=b^{1/2}$
$a=b^{1/2x}$
$b^y=\sqrt[3]{3c}$
$b^y=c^{1/3}$
$b=c^{1/3y}$
$c^z=a^{1/2}$
$c=a^{1/2z}=b^{1/4xz}$
$c^1=c^{1/12xyz}$
$1=\frac{1}{12xyz}$
$xyz=\frac{1}{12}$