i do not see any confusion sir.

I do know that x is raised to minus ten

Not a confusion. Whatever the power and X without parantheses is gonna always be a negative number as it is less than zero, as is said in the question root. y is determined to be positive as it is bigger than zero. All these lead us to choice B. However if x was between the brackets, it would assume positive value due to which it is to power an even number, 10.

Got this?

Not totally true because x is certainly negative. However, the power is even and the result is positive.

At this point the mental process is the follow

1) have a negative power I shift to the fraction

2) Now I have 1/x^10 and 1/y^5

x is negative but the power is even so the result is positive and y^5 as well

A this point all depends on the magnitude of x and y

x=1 and y =1000000 A is bigger.

Vice versa B is bigger

Carcass listen,

For the sign, the exponent does matter only when the base is between brackets... Only in that case, exponent has the power to change the sign of the base. In question, x is not covered with brackets. That means the exponent can only change the value of the base not the sign of it. Even power could have rendered the base positive IF sign was covered UNDER the even power.

(-1)^-10 is not same as -1^-10. The first is 1 and the second -1.

I would like to look up the book you got this question from, though.

Yes

Correct

Theoretically, if we do not put the x inside the bracket or rounded parenthesis, x is our base that has nothing to do with the sign minus.

I do not think is a sin in this case because when you deal with the fraction afterward x will be positive


However, you are correct and what you pointed out is that

Edited the question accordingly

The inequality \(x < 0 < y\) means \(x\) is negative, \(y\) is positive, and 0 lies between them.

Again my greetings Carcass,

In fact what I remember is that insofar as we are dealing with undefined numbers like x and y, it does not require brackets to have exponent change the sign. X is capable of covering the minus with no brackets. If, let say, x is -2, it is x that is -2, i.e., we are not allowed to isolate the sign from the number anymore. It is no longer extricable. We can in no wise consider -2 as 2 in the absence of brackets or the other way around. It is a given.

For instance, as far as I recall it, in a given equation like x^2+x+1, if we were provided with x being -2, then the result would automatically, with no help of brackets, be 3 rather than -5. That is how we were dealing with it in high school.

So, you were right, me wrong.