|2^3 - 15| - 5^2 - (-15) = ?

Understand the Problem

The question involves evaluating an expression that includes absolute values, exponents, and subtraction. It requires us to first simplify the components within the absolute value and then calculate the final result.

Answer

The answer is $-3$.

Steps to Solve

Calculate the exponentials

First, we calculate $2^3$ and $5^2$:

$$ 2^3 = 8 \ 5^2 = 25 $$

Substitute the exponential values into the expression

Now substituting these values into the expression:

$$ |8 - 15| - 25 - (-15) $$

Simplify inside the absolute value

Next, simplify inside the absolute value:

$$ 8 - 15 = -7 $$

So we have:

$$ |-7| - 25 - (-15) $$

Evaluate the absolute value

Calculate the absolute value:

$$ |-7| = 7 $$

Now the expression is:

$$ 7 - 25 + 15 $$

Combine the terms

Now, combine the remaining terms:

$$ 7 - 25 = -18 \ -18 + 15 = -3 $$

The final answer is $-3$.

More Information

This problem showcases the use of absolute values, order of operations, and handling negative numbers. Absolute values represent the distance from zero, so regardless of the original number's sign, the result is always non-negative.

Tips

Forgetting to evaluate the absolute value correctly. Ensure you always take the positive value of any negative result.
Miscalculating the order of operations, especially when adding or subtracting after handling absolute values.

AI-generated content may contain errors. Please verify critical information

Thank you for voting!