Evaluate 5⁰: Understanding the Zero Exponent Rule

Exponent Rules with Zero Powers

50= 5^0=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:03 Let's solve this problem together.
00:06 Remember, if any number, let's call it A, is raised to the power of zero, it equals one.
00:12 This only works if A is not zero.
00:16 Now, apply this rule to the question we have.
00:20 And there you have it, that's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

50= 5^0=

2

Step-by-step solution

We use the power property:

X0=1 X^0=1 We apply it to the problem:

50=1 5^0=1 Therefore, the correct answer is C.

3

Final Answer

1 1

Key Points to Remember

Essential concepts to master this topic
  • Zero Exponent Rule: Any non-zero number raised to zero equals 1
  • Application: 50=1 5^0 = 1 just like 70=1 7^0 = 1 or 1000=1 100^0 = 1
  • Verify: Use pattern recognition: 52=25 5^2 = 25 , 51=5 5^1 = 5 , 50=1 5^0 = 1

Common Mistakes

Avoid these frequent errors
  • Thinking zero exponent equals zero or the base number
    Don't assume 50=0 5^0 = 0 or 50=5 5^0 = 5 = wrong answer every time! Zero exponent doesn't mean "multiply by zero" or "keep the base." Always remember the zero exponent rule: 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?

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Think about the pattern when exponents decrease: 53=125 5^3 = 125 , 52=25 5^2 = 25 , 51=5 5^1 = 5 . Each time we divide by 5, so 50=5÷5=1 5^0 = 5 ÷ 5 = 1 !

Does this work for negative numbers too?

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Yes! (3)0=1 (-3)^0 = 1 and (10)0=1 (-10)^0 = 1 . The zero exponent rule applies to any non-zero number, positive or negative.

What about 0⁰? Does that equal 1 too?

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00 0^0 is actually undefined in most contexts! The zero exponent rule only applies to non-zero bases. Remember: any non-zero number to the zero power equals 1.

How can I remember this rule?

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Try this memory trick: "Zero power = One answer" or think of it as the neutral element - just like adding 0 doesn't change a number, any base to the zero power gives the multiplication neutral element: 1.

Is there a way to check my answer?

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Use the division pattern: Start with 52=25 5^2 = 25 , then 51=25÷5=5 5^1 = 25 ÷ 5 = 5 , then 50=5÷5=1 5^0 = 5 ÷ 5 = 1 . The pattern confirms our answer!

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