^=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
= [1 + 1/(-1)^2]^-1
= (1 + 1)^-1 = 1/2

Sure! Let's break down the expression step by step to understand how to solve it.

The expression we have is: (-1^2 + -1^-2)^-1

Step 1: Evaluate the exponents
First, let's focus on the exponents. The exponent symbol "^" indicates that we need to raise the base to the power of the exponent. In this case, we have -1 raised to the power of 2, which means (-1)^2.

(-1)^2 = (-1) * (-1) = 1

Similarly, we have -1 raised to the power of -2, which means (-1)^-2.

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

Therefore, now our expression becomes: (1 + 1)^-1

Step 2: Perform the addition
In this step, we simply perform the addition within the parentheses.

1 + 1 = 2

Our expression now becomes: 2^-1

Step 3: Evaluate the exponent
Finally, we evaluate the exponent by raising 2 to the power of -1.

2^-1 = 1 / 2

So, the value of the expression is 1/2.

Remember, when working with expressions involving exponents, it's important to follow the order of operations (also known as PEMDAS or BODMAS). This helps to ensure that the calculations are performed in the correct order.