^=exponents
/= divide
So I am not sure how to do this. It is an example in my book but I still don't get it. Can you work through ti so I can do my real work.
(-1^2+-1^-2)^-1
(-1^2+-1^-2)^-1 =
First, do work within the parentheses.
-1*-1 = 1 and -1-2 = 1/(-12) =
[1+(1/(-12)]= [1 + 1/1]-1 . (One moves the negative exponent in the numerator by making it 1/(the positive exponent; thus, -1-2 becomes 1/(-1)2.
Now flip the -1 exponent by taking the reciprocal.
[1/(1+1}] = 1/2
<Check my thinking. Check my arithmetic. There are so many exponents and negative exponents that it is easy to make a mistake. Furthermore, when I try to do the exponents it is easy to forget to turn the exponents off. I hope this turns out ok.
It looks ok but check my work anyway.
Sure, let's work through the problem step by step.
The expression is:
(-1^2+-1^-2)^-1
Step 1: Evaluate the exponents
-1^2 is equal to -1 squared, which is equal to 1.
-1^-2 is equal to 1 divided by (-1)^2, which is equal to 1 divided by 1, which is also 1.
So, (-1^2+-1^-2) becomes (1 + 1) = 2.
Step 2: Apply the negative exponent
Now, we have (2)^-1. To apply the negative exponent, we take the reciprocal of the base. So, (2)^-1 becomes 1/2.
Therefore, the final result is 1/2.
To check your work, you can substitute the original expression with the calculated value of (1/2) and verify if both sides of the equation are equal.
Thus, (-1^2+-1^-2)^-1 = 1/2.
I hope this helps you understand how to solve the problem! Let me know if you have any more questions.