do these cancel out and why/why not?
S^2 = S^2
S^-2 = S^2
do the same positive power 2 on both sides cancel out
or the opposite - and + powers
Somewhere in your math education, someone has led you astray. "Cancel out" is NOT in math terms, nor does it exist. Perhaps they meant "divide to unity".
example x/x does not cancel out, it divides to unity, so x/x = 1 as long as x is not zero.
Wash your mouth our with soap everytime it speaks "cancel out" .
s^2/s^2 is equal to one as long as s is not zero. if s is a zero, it is a maybe. Wait for the calculus of limits to understand that (example: sinx/x as x approaches zero....x cannot be zero in math rules of division)
s^2/s^-2=s^4.
I hope I "canceled out " your thinking on what "cancel out" means in math: Nothing.
To determine if the given expressions cancel out, we need to simplify and compare the two expressions.
First expression: S^2 = S^2
In this expression, we have the same base (S) with the same exponent (2) on both sides of the equation. Since any number raised to the power of 2 is equal to itself squared, we can simplify both sides:
S^2 = S^2
This means that the first expression does cancel out because both sides of the equation are equal.
Second expression: S^-2 = S^2
In this expression, we have a base (S) with different exponents (-2 and 2) on either side of the equation. To simplify this, we need to apply the rules of exponentiation:
When a number has a negative exponent, it can be flipped to become the reciprocal of the positive exponent. Therefore, S^-2 is equal to 1/S^2. The second expression can now be written as:
1/S^2 = S^2
These two expressions do not cancel out because they are not equal to each other. The first expression represents the square of S, while the second expression represents the reciprocal of the square of S.