Question

What is the answer for this problem in the picture

Answer 1

The correct answer is third option

8x⁴yz⁴√2yz

Explanation:

It is given that,

√128x⁸y³z⁹

To find the equivalent of √128x⁸y³z⁹

We have 128 = 2⁷

x⁸ = (x⁴)², y³ = y² * y and z⁹ = (z⁴)² * z

√128x⁸y³z⁹ = √(2⁷ * (x⁴)² * y²y * (z)⁴)²z)

= 2³x⁴yz⁴√(2 * y * z)

= 8x⁴yz⁴√2yz

Therefore the correct answer is third option

Answer 2

The correct answer option is
`= 8 x ^ 4 y z ^ 4 √(2yz)`.

Explanation:

We are given the following expression and we are to simplify it and determine whether which of the given expressions is equivalent to it, assuming
`y\geq 0` and
`z\geq 0`:

`\sqrt { 128 x ^ 8 y ^ 3 z ^ 9 }`

Breaking the terms to get:

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

`= 8 x ^ 4 y z ^ 4 √(2yz)`