If none of x, y, & z equals to 0, is x^4y^5z^6 > 0?

For \(x^4y^5z^6 > 0\) to be true, \(x^4\), \(y^5\) and \(z^6\) have to be all positive numbers.

x and z could be negative numbers themselves but their positive even powers will turn them into positive numbers.

The real question here is if y is a positive number or negative.

(1) \(y > x^4\)

\(x^4\) we know is an even number because of the positive even power of x and if y is greater than that, it means y is a positive number.

Thus, Positive x Positive x Positive > 0

SUFFICIENT


(2) \(y > z^5\)

If z is positive, \(z^5\) will be positive and a y greater than that will be positive too. That will result in Even x Even x Even > 0

However, if z is negative, \(z^5\) will be negative as well and a y greater than that could either be negative or positive.

Thus, Positive x Negative x Positive < 0

INSUFFICIENT

The answer is A.

\(x^4\) and \(z^6\)yields a positive result . thus we all about need to know whether y is positive.

Statement 1: \(y>x^4\). \(x^4\) will always be positive. thus y has to be positive. Sufficient.

Statement : \(y>z^5\). NOT clear. z= -2.\(z^5 = -32\) and y = -2. NOT sufficient.

The best answer is A.