Evaluate -(-2)³: Working with Negative Numbers and Exponents

Q: Why is (-2)³ negative when I'm cubing a number?

When you cube a negative number, you get a negative result because you multiply an odd number of negative factors: $(-2) \times (-2) \times (-2) = -8$. Remember: odd powers of negatives stay negative!

Q: What's the difference between -2³ and (-2)³?

Big difference! $-2^3 = -(2^3) = -8$ (negative applied after), but $(-2)^3 = (-2) \times (-2) \times (-2) = -8$ (negative is part of the base). The parentheses matter!

Q: How do I handle the double negative in -(-8)?

Double negatives become positive! Think of it as "the opposite of negative 8" which equals positive 8. So $-(-8) = +8$.

Q: What if the exponent was even instead of 3?

With even exponents, $(-2)^2 = 4$ (positive), so $-(-2)^2 = -4$. Even powers of negative numbers are always positive, odd powers stay negative.

Q: Can I just ignore the parentheses around -2?

Never ignore parentheses! They show that the negative sign is part of the base being raised to the power. Without them, you'd calculate $-2^3 = -8$ instead of $(-2)^3 = -8$.

Negative Exponents with Order of Operations

$-(-2)^3=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve the problem together.

00:08 First, let's figure out the sign.

00:11 An odd power means the sign will be negative.

00:20 Now, let's calculate the power of the number.

00:29 Remember, negative times negative gives a positive result.

00:34 And that's how we find the solution to the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$-(-2)^3=$

Step-by-step solution

To solve the expression $-(-2)^3$ , we need to first calculate the inner power and then apply the outer negative sign.

Step 1: Calculate $(-2)^3$ .
Since $(-2)$ is raised to the power of 3, we perform the multiplication: $(-2) \times (-2) \times (-2)$ .
$(-2) \times (-2) = 4$ .
Continuing, $4 \times (-2) = -8$ .
Thus, $(-2)^3 = -8$ .
Step 2: Apply the outer negative sign.
We have $-(-2)^3 = -(-8)$ .
According to arithmetic rules, a negative times a negative becomes positive, so $-(-8) = 8$ .

Therefore, the solution to the problem is $8$ , which matches choice number 2.

Final Answer

$8$

Key Points to Remember

Essential concepts to master this topic

Order: Calculate exponent first, then apply outer negative sign
Technique: $(-2)^3 = (-2) \times (-2) \times (-2) = -8$
Check: Verify final sign: $-(-8) = +8$ ✓

Common Mistakes

Avoid these frequent errors

Applying the negative sign before calculating the exponent
Don't calculate $-(-2)^3$ as $-(+2)^3 = -8$ ! This ignores order of operations and gives the wrong sign. Always calculate the exponent $(-2)^3$ first, then apply the outer negative.

Practice Quiz

Test your knowledge with interactive questions

$$ (-2)^7= $$

FAQ

Everything you need to know about this question

Why is (-2)³ negative when I'm cubing a number?

When you cube a negative number, you get a negative result because you multiply an odd number of negative factors: $(-2) \times (-2) \times (-2) = -8$ . Remember: odd powers of negatives stay negative!

What's the difference between -2³ and (-2)³?

Big difference! $-2^3 = -(2^3) = -8$ (negative applied after), but $(-2)^3 = (-2) \times (-2) \times (-2) = -8$ (negative is part of the base). The parentheses matter!

How do I handle the double negative in -(-8)?

Double negatives become positive! Think of it as "the opposite of negative 8" which equals positive 8. So $-(-8) = +8$ .

What if the exponent was even instead of 3?

With even exponents, $(-2)^2 = 4$ (positive), so $-(-2)^2 = -4$ . Even powers of negative numbers are always positive, odd powers stay negative.

Can I just ignore the parentheses around -2?

Never ignore parentheses! They show that the negative sign is part of the base being raised to the power. Without them, you'd calculate $-2^3 = -8$ instead of $(-2)^3 = -8$ .

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