Find the values for a, b, and c that complete the simplification.

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]

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