Question

What expression is equivalent to? Screenshots attached. Please help!

Answer 1

the correct option is C i.e.
`8x^4yz^4√(2yz)`

Explanation:

We need to solve the expression :

`√(128x^8y^3z^9)`

Factors of 128 are: 2x2x2x2x2x2x2

and we know √ = 1/2

and √a.b = √a.√b

Solving:

`=√(128x^8y^3z^9)\\\\=√(128) √(x^8) √(y^3) √(z^9)\\=√(2x2x2x2x2x2x2)√(x^8) √(y^2.y) √(z^8.z)\\=√(2^2x2^2x2^2x2)√(x^8) √(y^2.y) √(z^8.z)\\=(2^2)^(1/2) (2^2)^(1/2)(2^2)^(1/2) (2)^(1/2) (x^8)^(1/2) (y^2)^(1/2) (y)^(1/2) (z^8)^(1/2) z^(1/2)\\=2.2.2.(2)^(1/2)x^4y(y)^(1/2)z^4(z)^(1/2)\\=8x^4yz^4√(2yz)`

So, the correct option is C i.e.
`8x^4yz^4√(2yz)`