Question

If $x=y^a,y=z^b,z=x^c$ then find abc. [4 MARKS]

Answer 1

Concept : 1 Mark
Application : 1 Mark
Calculation : 2 Marks

$x=y^a$

$=(z^b{)}^a$ $(\because y=z^b)$

$=z^{ab}$

$=(x^c{)}^{ab}$ $(\because x^c=z)$

$x=x^{abc}$ $\left(\right(a^m{)}^n=a^{mn})$

$\Rightarrow x^1=x^{abc}$

As bases are equal, exponents are equal.

$\Rightarrow abc=1$