Question

What is the answer for this problem in the picture

Answer 1

Answer:

The correct answer is third option

8x⁴yz⁴√2yz

Step-by-step 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

Answer:

The correct answer option is $= 8 x ^ 4 y z ^ 4 \sqrt{2yz}$.

Step-by-step 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\sqrt{2yz} \times x^{8\times\frac{1}{2} } \times y^{2\times \frac{1}{2} } \times z^{8\times \frac{1}{2} }$

$= 8 x ^ 4 y z ^ 4 \sqrt{2yz}$