Can anyone please help me with some simple exponent questions?

Question

(I must use / for the radical sign)

Why does /-x^2 = -x if you're multiplying -x times -x wouldn't you get +x? Obviously you must be multiplying -x times +x but why would you do that if you're supposed to be multiplying the number by itself??

Second question is, does /-x^3 = +y or -y????

Third question is, /-x ^-2 = +x or -x????

Fourth question is /-x^-3 = +y or -y????

Fifth question is, does /x^-2 = +y or -y????

Thanks for taking the time to answer these for me.

I quote from the math book "-x^2 = -x but you are saying it = +x??

The 2nd question I'm asking if you plug in a 5 for example as x /-5^3 you get 125 but is it +125 or -125?

The 3rd one I wanted the end number or fraction with NO exponent. I wanted to know whether it would be + or -.

The 4th one I'm asking for y because I wanted the exponent gone in the denomenator. Will it be a positive or negative with NO exponent?

Same with the last one, is it + or - with NO exponent. Thanks.

To TychaBrahe - I think you misunderstood. These are each under a radical sign. I had to use the / as a radical sign. The -x^2 is under a radical sign and so are the rest of the examples. Thanks.

The first thing I wrote under details where I quoted from the book was all under a radical sign.

Answer 1

Hey. I think that you are confusing things

1) There is not a root of (-x^2) if you work in R, the set of the real numbers. The same way there is not a root of any negative number or expression if you work in R.

..... 3
2) V(-x^3) = -x ( I mean "cubic root of (x^3)" )

Why?

Because (-x)(-x)(-x) = -x^3

3) If you read in your book things like:

y =V(x^2) or y = V(-x^3), what is ment is something different. y = f(x)

So: the books means:

f(x) = V (x^2) = |x| , where |x| = absolute value of x = abs (x)

If x belongs to R+, the set of the positive numbers, then you dont have to use abs, but this is only because you are working in a positive set of numbers

4) x^(-2) = 1 / x^2

So, V[x^(-2)] = V(1/x^2) = V1 / V(x^2) = 1/|x|

This is valid forall x different from 0, x a real number.

5) V4 = 2, and not -2

In fact, (-2)(-2) = 4, but, if you consider the definition of function, you will realise that you cant have 2 values of V4 if you want f(x) = Vx to be a function.

In fact, thats why in the quadratic equation you have to write +/- V (b^2-4ac). This wouldnt make any sense if the root would already give us a positive and a negative result.

6) This is wrong:

sqrt(-x^2) = sqrt(x^2) = x

sqrt(-x)^3 is not equals to (sqrt(x)i)^3, is equals to sqrt (ix)^3.

And its not the same (-x)^2 = x^2 than - x^2 = - (x^2)

Write to me and I will be glad to help you.

Ilusión

Answer 2

I'm not real sure I understand exactly what you're asking in a couple of places, but here goes:

√(-x²) does **not** equal -x. It equals ±ix (where i is the 'unit imaginary' number)

The rest of them that involve taking the square root of a negative value have similar answers. The --definition-- of a square root is 'one of two equal factors of the original number'. As a result, both 2 and -2 are square roots of 4. In fact, you will frequently see √a² = ±a toi emphasize this point. But a negative number cannot have a square root (at least, over the integers) since no 2 'equal' factors exist for, say, -9. It can only be a product of +3 and -3 which are not equal.

Doug

Answer 3

It does supply the identical reply, however now not for the cause you mentioned it does. (-four)^three does identical (-four)(-four)(-four), that is -sixty four. However, -four^three equals (-a million)(four)(four)(four). If the terrible isn't incorporated within the parentheses with the time period that's being suffering from the exponent, you then observe it afterwards. So on this case it's four^three instances -a million, or the reverse of four^three. Since four^three is sixty four, your reply is once more -sixty four. -x^n most effective equals (-x)^n whilst n (the exponent) is strange. For illustration, -four^two equals -sixteen, given that the terrible is available in after the squaring. However, (-four)^two equals sixteen, given that (-four)(-four)=sixteen. An convenient option to consider that is PEMDAS. When there are parentheses, you need to do the parenthesis first, that is why you dice (-four), and now not simply four. However, whilst there are not any parentheses, you do the exponents first. In the case of the hindrance you gave, the exponent applies most effective to the four, given that quite the expression is (-a million)(four)^three. So you do the exponent first and you then multiply.

Answer 4

It really helps if you use parentheses.

If you are asking
sqrt(-x)^2 = -x,

Then this is because
sqrt(-4) = 2i.
(2i)^2 = -4

But another way to read what you typed is
sqrt(-x^2) = sqrt(x^2) = x

Second problem: I don't know where the y comes in.
sqrt(-x)^3 = (sqrt(x)i)^3 = sqrt(x)^3*i^3 = x^(3/2) * -i = -x^(3/2)
sqrt(-x^3) = -x^(3/2)

And it just gets worse from there. In the third question, are you taking the square root of -(x^(-2)) or (-x)^(-2) or taking the square root of the square root of -x?

Answer 5

1) -x * -x = +x^2

2) Question doesn't make sense

3) -x^-2 is the same as (1 / -x^2)

4) Why are you asking id they equal 'y'
-x^-3 is the same as (1 / -x^3)

5) x^-2 is the same as (1 / +x^2)