Question

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

Answer 1

a = 6, b = 4, c = 2

Step-by-step explanation

see attached

Answer 2

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

Explanation:

The given expression is

`\sqrt{x^(12)y^(9)z^(5)}=(x^(a)y^bz^c)√(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)√(yz)` .... (2)
`[\because √(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.