Answer :
To solve the given problem step by step, we need to evaluate each term and then combine them. Let's start by breaking down the expression [tex]\( 12^2 + (-1)^{501} \)[/tex].
### Step 1: Evaluate [tex]\( 12^2 \)[/tex]
First, we need to calculate [tex]\( 12^2 \)[/tex].
[tex]\[ 12^2 = 12 \times 12 = 144 \][/tex]
So, [tex]\( 12^2 \)[/tex] equals 144.
### Step 2: Evaluate [tex]\( (-1)^{501} \)[/tex]
Next, we have to evaluate [tex]\( (-1)^{501} \)[/tex].
The pattern for the power of [tex]\((-1)\)[/tex] is that:
- When raised to an even exponent, it is [tex]\(1\)[/tex].
- When raised to an odd exponent, it is [tex]\(-1\)[/tex].
Since 501 is an odd number, we have:
[tex]\[ (-1)^{501} = -1 \][/tex]
### Step 3: Sum the terms
Now, we sum the results obtained in the previous steps:
[tex]\[ 144 + (-1) \][/tex]
When you add these together, you get:
[tex]\[ 144 - 1 = 143 \][/tex]
### Final Answer
Thus, the final result of the expression [tex]\( 12^2 + (-1)^{501} \)[/tex] is:
[tex]\[ \boxed{143} \][/tex]
### Step 1: Evaluate [tex]\( 12^2 \)[/tex]
First, we need to calculate [tex]\( 12^2 \)[/tex].
[tex]\[ 12^2 = 12 \times 12 = 144 \][/tex]
So, [tex]\( 12^2 \)[/tex] equals 144.
### Step 2: Evaluate [tex]\( (-1)^{501} \)[/tex]
Next, we have to evaluate [tex]\( (-1)^{501} \)[/tex].
The pattern for the power of [tex]\((-1)\)[/tex] is that:
- When raised to an even exponent, it is [tex]\(1\)[/tex].
- When raised to an odd exponent, it is [tex]\(-1\)[/tex].
Since 501 is an odd number, we have:
[tex]\[ (-1)^{501} = -1 \][/tex]
### Step 3: Sum the terms
Now, we sum the results obtained in the previous steps:
[tex]\[ 144 + (-1) \][/tex]
When you add these together, you get:
[tex]\[ 144 - 1 = 143 \][/tex]
### Final Answer
Thus, the final result of the expression [tex]\( 12^2 + (-1)^{501} \)[/tex] is:
[tex]\[ \boxed{143} \][/tex]
