Understanding Exponents: Simplify the Problem 2^0 Divided by 3

Q: Why does any number to the power of 0 equal 1?

Think of it this way: $ 2^3 = 8 $, $ 2^2 = 4 $, $ 2^1 = 2 $. Each time we decrease the exponent by 1, we divide by 2. So $ 2^0 = 2^1 ÷ 2 = 2 ÷ 2 = 1 $!

Q: Does this rule work for negative numbers too?

Yes! $ (-5)^0 = 1 $, $ (-100)^0 = 1 $. The zero exponent rule applies to any non-zero number, whether positive or negative.

Q: What about 0 to the power of 0?

$ 0^0 $ is a special case that's undefined in basic math. For now, just remember the rule works for all non-zero numbers only.

Q: How is this different from 2 times 0?

$ 2^0 $ means exponent (2 raised to the power of 0), while $ 2 \times 0 $ means multiplication. These are completely different operations with different results!

Q: Can I just memorize that the answer is always 1/3?

No! The denominator changes the final answer. $ \frac{2^0}{3} = \frac{1}{3} $, but $ \frac{2^0}{5} = \frac{1}{5} $. Always apply the zero exponent rule first, then divide.

Zero Exponents with Fraction Division

$\frac{2^0}{3}=$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Any number(M) raised to the power of 0 exponent, always equals 1

00:07 This formula is valid, as long as the base is not 0

00:10 We'll use this formula in our exercise, we can see that the base is not 0

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

$\frac{2^0}{3}=$

Step-by-step solution

To solve the problem $\frac{2^0}{3}$ , follow these steps:

Step 1: Identify the given expression – The numerator is $2^0$ .
Step 2: Apply the Zero Exponent Rule – By the rule $a^0 = 1$ for any non-zero number $a$ , we have $2^0 = 1$ .
Step 3: Simplify the expression – Replace $2^0$ with 1 to get $\frac{1}{3}$ .

Therefore, the value of the expression $\frac{2^0}{3}$ is $\frac{1}{3}$ .

Final Answer

$\frac{1}{3}$

Key Points to Remember

Essential concepts to master this topic

Zero Exponent Rule: Any non-zero number raised to power 0 equals 1
Technique: Replace $2^0$ with 1, then calculate $\frac{1}{3}$
Check: Verify $2^0 = 1$ , so $\frac{1}{3}$ is correct ✓

Common Mistakes

Avoid these frequent errors

Thinking any number to the power of 0 equals 0
Don't assume $2^0 = 0$ = $\frac{0}{3} = 0$ ! This confuses the zero exponent rule with multiplication by zero. Always remember that any non-zero number raised to the power of 0 equals 1, not 0.

Practice Quiz

Test your knowledge with interactive questions

Which of the following is equivalent to $$ 100^0 $$ ?

FAQ

Everything you need to know about this question

Why does any number to the power of 0 equal 1?

Think of it this way: $2^3 = 8$ , $2^2 = 4$ , $2^1 = 2$ . Each time we decrease the exponent by 1, we divide by 2. So $2^0 = 2^1 ÷ 2 = 2 ÷ 2 = 1$ !

Does this rule work for negative numbers too?

Yes! $(-5)^0 = 1$ , $(-100)^0 = 1$ . The zero exponent rule applies to any non-zero number, whether positive or negative.

What about 0 to the power of 0?

$0^0$ is a special case that's undefined in basic math. For now, just remember the rule works for all non-zero numbers only.

How is this different from 2 times 0?

$2^0$ means exponent (2 raised to the power of 0), while $2 \times 0$ means multiplication. These are completely different operations with different results!

Can I just memorize that the answer is always 1/3?

No! The denominator changes the final answer. $\frac{2^0}{3} = \frac{1}{3}$ , but $\frac{2^0}{5} = \frac{1}{5}$ . Always apply the zero exponent rule first, then divide.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Powers - special cases questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime