Evaluate the Fractional Expression: What is 1 Divided by 5 Raised to Power Zero?

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

Think of exponent patterns: $ 5^3 = 125 $, $ 5^2 = 25 $, $ 5^1 = 5 $. Each time we decrease the exponent by 1, we divide by 5. So $ 5^0 = 5^1 ÷ 5 = 5 ÷ 5 = 1 $!

Q: What if the base was 0 instead of 5?

$ 0^0 $ is actually undefined in most contexts! The zero exponent rule only applies to non-zero bases. Remember: we need a non-zero number for the rule to work.

Q: Does this work with negative numbers too?

Yes! $ (-3)^0 = 1 $, $ (-100)^0 = 1 $. Any non-zero number (positive or negative) raised to the zero power equals 1.

Q: How is this different from 1 divided by 5?

Great observation! $ \frac{1}{5^0} $ equals 1, but $ \frac{1}{5} $ equals 0.2. The key difference is that $ 5^0 = 1 $ in the denominator, not 5!

Q: What if I see a more complex expression like (2x)⁰?

As long as the entire base $ (2x) $ is non-zero, then $ (2x)^0 = 1 $. The zero exponent rule applies to the entire expression in the base!

Zero Exponents with Fractional Expressions

$\frac{1}{5^0}=$

❤️ 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

00:04 Any number(M) to the power of 0 always equals 1

00:10 This formula is valid as long as the base is not 0

00:14 We will use this formula in our exercise, we can see that the base is not 0

00:22 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

$\frac{1}{5^0}=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given expression which is $\frac{1}{5^0}$ .
Step 2: Recognize that $5^0$ involves a zero exponent.
Step 3: Apply the zero exponent rule, which states that any non-zero number raised to the power of zero equals one.
Step 4: Substitute the result back into the original expression.

Now, let's work through each step:
Step 1: The problem gives us $\frac{1}{5^0}$ .
Step 2: We apply the zero exponent rule to the term $5^0$ . According to the rule, $5^0 = 1$ .
Step 3: Substitute this value into the expression, thus yielding $\frac{1}{1}$ .
Step 4: Perform the division, which results in $1$ .

Therefore, the solution to the problem is 1.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Zero Exponent Rule: Any non-zero number raised to power zero equals one
Technique: Replace $5^0$ with 1, then simplify $\frac{1}{1} = 1$
Check: Verify that $5^0 = 1$ before dividing: $\frac{1}{1} = 1$ ✓

Common Mistakes

Avoid these frequent errors

Thinking zero exponents equal zero
Don't assume $5^0 = 0$ giving $\frac{1}{0}$ = undefined! Zero exponents don't make the base zero - they make any non-zero base equal to 1. Always remember: any non-zero number to the zero power equals 1.

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 zero power equal 1?

Think of exponent patterns: $5^3 = 125$ , $5^2 = 25$ , $5^1 = 5$ . Each time we decrease the exponent by 1, we divide by 5. So $5^0 = 5^1 ÷ 5 = 5 ÷ 5 = 1$ !

What if the base was 0 instead of 5?

$0^0$ is actually undefined in most contexts! The zero exponent rule only applies to non-zero bases. Remember: we need a non-zero number for the rule to work.

Does this work with negative numbers too?

Yes! $(-3)^0 = 1$ , $(-100)^0 = 1$ . Any non-zero number (positive or negative) raised to the zero power equals 1.

How is this different from 1 divided by 5?

Great observation! $\frac{1}{5^0}$ equals 1, but $\frac{1}{5}$ equals 0.2. The key difference is that $5^0 = 1$ in the denominator, not 5!

What if I see a more complex expression like (2x)⁰?

As long as the entire base $(2x)$ is non-zero, then $(2x)^0 = 1$ . The zero exponent rule applies to the entire expression in the base!

🌟 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