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