Why does the ³ and the ² influence wether it is a (-) or the (+)????

Question

Ex.

(y-x)²=[-(x-y)]²= ?(x-y)²

How do you know it's a positive knowing the it is even ²?

ex.2

(y-x)³=[-(x-y)]³= ?(x-y)³

How do you know it's a negative?

Answer 1

You need to understand what the exponents mean. When we raise something to a power, we are saying to multiply it a number of times.

5^2 = 5 * 5 = 25
5^3 = 5 * 5 * 5 = 125
5^4 = 5 * 5 * 5 * 5 = 625
etc.

Now for positive and negative numbers, you need to know the following:

positive * positive = positive
positive * negative = negative
negative * positive = negative
negative * negative = positive

Automatically, any positive number raised to any power will result in a positive number. With the negatives, it depends on whether or not the exponent is odd or even. Look what happens:

(-3)^1 = -3
(-3)^2 = -3 * -3 = 9
(-3)^3 = -3 * -3 * -3 = 3 * -3 = -27
(-3)^4 = -3 * -3 * -3 * -3 = 9 * -3 * -3 = -27 * -3 = 81
etc.

So as you can see, even exponents will result in a positive number, odd exponents results in a negative number.

Answer 2

When something is multiplied by itself (or is raised to the power of 2), whether it is positive or negative, the square must be posititive (because a negative times a negative is a positive). However, when the square of a number is again multiplied by itself (or is raised to the power of 3), if the original number is positive, the cube is positive, while if it is negative, the cube would be negative (-x times -x times -x = -x3)

Answer 3

Well anything that is to the even power becomes positive (-1)^2. Is positive.

Things that are to the odd power do not change signs (think of (-1)^1 is still negative)

However -(1)^2 is still negatve because you first square then multiply negative one.

Answer 4

[-(x-y)]² = -(x-y) * -(x-y) = - * - = +

[-(x-y)]³ = -(x-y) * -(x-y) * -(x-y) = - * - * - = -

even always is positive.
odd always is negative.

just like + * - is equivalent to an odd. and + * + and - * - are both even.