Comparing Absolute Values: Is -|-64| Equal to |8²|?

To solve this problem, we'll follow these steps:

• Step 1: Calculate the absolute value of $-64$.
• Step 2: Apply the negative sign to the absolute value calculated.
• Step 3: Calculate the absolute value of $8^2$.
• Step 4: Compare the two numbers to determine if they are opposites.

Now, let's work through each step:

Step 1: Calculate $\left|-64\right|$.
The absolute value of $-64$ is $|-64| = 64$.

Step 2: Apply the negative sign to this absolute value.
$-\left|-64\right| = -64$

Step 3: Calculate $\left|8^2\right|$.
First, compute $8^2 = 64$. Then, calculate $|64| = 64$.

Step 4: Compare the numbers.
We have $-64$ from Step 2 and $64$ from Step 3. These two numbers are opposites because the opposite of $64$ is $-64$.

Therefore, the two numbers are indeed opposites.