Question

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

Answer 1

Answer:

a = 6, b = 4, c = 2

Step-by-step explanation

see attached

Answer 2

Answer:

The required values are 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)       $[\because \sqrt{x^2}=x]$

From (1) and (2), we get

$a=6,b=4,c=2$

Therefore the required values are a=6, b=4 and c=2.