Solve (-3)^0: Evaluating a Negative Base with Zero Exponent

Q: Does it matter that the base is negative?

No! The zero exponent rule works for any non-zero number, whether it's positive or negative. So $ 3^0 = 1 $ and $ (-3)^0 = 1 $ and even $ (-999)^0 = 1 $.

Q: What if the base was 0 instead?

That's different! $ 0^0 $ is actually undefined in mathematics. The zero exponent rule only applies to non-zero bases. Since our base is -3 (not zero), we're safe to use the rule.

Q: How can I remember this rule?

Try this memory trick: "Zero power makes everything ONE-derful!" Any non-zero number raised to the zero power becomes 1, no matter how big, small, or negative the base is.

Q: Is this the same as multiplying by zero?

No way! Multiplying by zero gives you zero, but raising to the zero power gives you one. These are completely different operations: $ (-3) \times 0 = 0 $ but $ (-3)^0 = 1 $.

Zero Exponent Rule with Negative Base

Solve the following problem:

$\left(-3\right)^0=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Simply

00:03 According to the laws of exponents, any number raised to the power of 0 always equals 1:

00:07 We will use this formula in our exercise

00:13 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 problem:

$\left(-3\right)^0=$

Step-by-step solution

To solve this problem, let's follow these steps:

Understand the zero exponent rule.
Apply this rule to the given expression.
Identify the correct answer from the given options.

According to the rule of exponents, any non-zero number raised to the power of zero is equal to $1$ . This is one of the fundamental properties of exponents.
Now, apply this rule:

Step 1: We are given the expression $(-3)^0$ .
Step 2: Here, $-3$ is our base. We apply the zero exponent rule, which tells us that $(-3)^0 = 1$ .

Therefore, the value of $(-3)^0$ is $1$ .

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Rule: Any non-zero number raised to the power zero equals one
Technique: Apply the rule directly: $(-3)^0 = 1$
Check: The base is non-zero (-3 ≠ 0), so the rule applies perfectly ✓

Common Mistakes

Avoid these frequent errors

Confusing the zero exponent rule with multiplication by zero
Don't think (-3)^0 = 0 because zero is in the exponent = wrong answer of 0! Zero in the exponent means "multiply the base by itself zero times," which equals 1. Always remember: any non-zero base to the power of zero equals 1.

Practice Quiz

Test your knowledge with interactive questions

$112^0=\text{?}$

FAQ

Everything you need to know about this question

Why does any number to the power of zero equal 1?

Think of it this way: when you divide powers with the same base, you subtract exponents. So $\frac{(-3)^2}{(-3)^2} = (-3)^{2-2} = (-3)^0$ . But any number divided by itself equals 1, so $(-3)^0 = 1$ !

Does it matter that the base is negative?

No! The zero exponent rule works for any non-zero number, whether it's positive or negative. So $3^0 = 1$ and $(-3)^0 = 1$ and even $(-999)^0 = 1$ .

What if the base was 0 instead?

That's different! $0^0$ is actually undefined in mathematics. The zero exponent rule only applies to non-zero bases. Since our base is -3 (not zero), we're safe to use the rule.

How can I remember this rule?

Try this memory trick: "Zero power makes everything ONE-derful!" Any non-zero number raised to the zero power becomes 1, no matter how big, small, or negative the base is.

Is this the same as multiplying by zero?

No way! Multiplying by zero gives you zero, but raising to the zero power gives you one. These are completely different operations: $(-3) \times 0 = 0$ but $(-3)^0 = 1$ .

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