For this problem, we are going to have to use our order of operations, which is: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction (often abbreviated PEMDAS).
First, let's see if there are any parentheses. There is one set of parentheses which we will have to remove. To do this, we will simply multiply the -4 by the 6, given us a value of -24 to take the place of the -4(6). Now our problem is:
[tex] \dfrac{12^2 - 24 + 1}{11^2} [/tex]
Next, we will check for exponents. There are exponents, so we will need to take care of those. [tex] 12^2 [/tex] is equal to 144, and [tex] 11^2 [/tex] is equal to 121. We can now substitute these values into the original expression to get:
[tex] \dfrac{144 - 24 + 1}{121} [/tex]
Now, we will check for any multiplication or division. Besides the entire expression (which is a fraction), there is none, so we will move on to the next step: Addition and Subtraction. You can see there is addition and subtraction in the numerator. [tex] 144 - 24 [/tex] is equal to 120, and [tex] 120 + 1 [/tex] is equal to 121. Our problem is now:
[tex] \dfrac{121}{121} = \boxed{1} [/tex]
Our answer is 1.
