Question

Which expression is equivalent to √128x^8y^3z^9? Assume x>0 and y>0.

Answer 1

C is the correct answer :)

Answer 2

Answer: The correct option is (C)
`8x^4yz^4√(2yz).`

Step-by-step explanation: We are given to select the correct expression that is equivalent to the expression below:

`E=√(128x^8y^3z^9).`

We will be using the following properties of exponents:

`(i)~\sqrt a=a^(1)/(2),\\\\(ii)~(ab)^x=a^xb^x,\\\\(iii)~(a^x)^y=a^(x* y).`

Since y > 0 and z > 0, so we will be considering the positive square root of y and z.

We have

`E\\\\=√(128x^8y^3z^9)\\\\=(128x^8y^3z^9)^(1)/(2)\\\\=(128)^(1)/(2)(x^8)^(1)/(2)(y^3)^(1)/(2)(z^9)^(1)/(2)\\\\=(2* 8^2)^(1)/(2)x^{8* (1)/(2)}y^{3*(1)/(2)}z^{9*(1)/(2)}\\\\=8x^4yz^4(2yz)^(1)/(2)\\\\=8x^4yz^4√(2yz).`

Thus, the equivalent expression is
`8x^4yz^4√(2yz).`

(C) is the correct option.