Solve the Exponent Problem: Finding (-8)² Using Order of Operations

Q: What's the difference between (-8)² and -8²?

With parentheses, $ (-8)^2 = 64 $ because you square the entire negative number. Without parentheses, $ -8^2 = -64 $ because you square 8 first, then apply the negative sign.

Q: Why does negative times negative equal positive?

Think of it as opposite directions: if negative means "backwards," then going backwards twice brings you forward! Mathematically, $ (-8) \times (-8) = +64 $.

Q: How do I remember when the answer is positive or negative?

For even exponents (like 2, 4, 6), negative numbers always become positive. For odd exponents (like 1, 3, 5), negative numbers stay negative.

Q: What if I see something like (-8)³?

With an odd exponent, the result stays negative: $ (-8)^3 = (-8) \times (-8) \times (-8) = -512 $. The extra negative factor makes the final result negative.

Q: Is there a quick way to check my work?

Yes! For even exponents with negative bases, your answer should always be positive. If you got a negative result, double-check your calculation!

Exponent Operations with Negative Base

Solve the following expression:

$(-8)^2=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 First, let's calculate the sign

00:06 Even power, therefore the sign will be positive

00:12 Now let's calculate the power

00:15 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following expression:

$(-8)^2=$

Step-by-step solution

When we have a negative number raised to a power, the location of the minus sign is very important.

If the minus sign is inside or outside the parentheses, the result of the exercise can be completely different.

When the minus sign is inside the parentheses, our exercise will look like this:

(-8)*(-8)=

Since we know that minus times minus is actually plus, the result will be positive:

(-8)*(-8)=64

Final Answer

$64$

Key Points to Remember

Essential concepts to master this topic

Rule: Parentheses determine what gets raised to the power
Technique: $(-8)^2 = (-8) \times (-8) = 64$
Check: Negative times negative equals positive: $(-8)^2 = 64$ ✓

Common Mistakes

Avoid these frequent errors

Ignoring parentheses when squaring negative numbers
Don't calculate $-8^2 = -64$ instead of $(-8)^2 = 64$ ! Without parentheses, only the 8 gets squared, then the negative sign is applied. Always square the entire negative number when it's in parentheses.

Practice Quiz

Test your knowledge with interactive questions

$$ (-2)^7= $$

FAQ

Everything you need to know about this question

What's the difference between (-8)² and -8²?

With parentheses, $(-8)^2 = 64$ because you square the entire negative number. Without parentheses, $-8^2 = -64$ because you square 8 first, then apply the negative sign.

Why does negative times negative equal positive?

Think of it as opposite directions: if negative means "backwards," then going backwards twice brings you forward! Mathematically, $(-8) \times (-8) = +64$ .

How do I remember when the answer is positive or negative?

For even exponents (like 2, 4, 6), negative numbers always become positive. For odd exponents (like 1, 3, 5), negative numbers stay negative.

What if I see something like (-8)³?

With an odd exponent, the result stays negative: $(-8)^3 = (-8) \times (-8) \times (-8) = -512$ . The extra negative factor makes the final result negative.

Is there a quick way to check my work?

Yes! For even exponents with negative bases, your answer should always be positive. If you got a negative result, double-check your calculation!

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