Answer:
a = 6, b = 4, and c = 2
Step-by-step explanation:
The given expression is
\sqrt{x^{12}y^{9}z^{5}}=(x^{a}y^bz^c)\sqrt{yz} .... (1)
It can be written as
\sqrt{x^{12}\cdot y^{8}\cdot y\cdot z^{4}\cdot z}
\sqrt{x^{12}\cdot y^{8}\cdot z^{4}\cdot y\cdot z}
\sqrt{(x^{6})^2\cdot (y^{4})^2\cdot (z^{2})^2\cdot y\cdot z} [\because (a^m)^n=a^{mn}]
\sqrt{(x^{6}y^4z^2)^2\cdot y\cdot z} [\because a^xb^x=(ab)^x]
(x^{6}y^4z^2)\sqrt{yz} .... (2) [\because \sqrt{x^2}=x]
