Evaluate 112^0: Understanding the Zero Exponent Rule

Exponent Rules with Zero Power

1120=? 112^0=\text{?}

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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.
00:07 Here's an important rule to remember: when any number is raised to the power of zero, the result is always 1.
00:14 Just keep in mind that this rule works for all numbers except zero. Zero is a special case.
00:21 Now, let's use this rule in our problem.
00:24 And there we have our solution! Remember, anything to the power of zero equals 1.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

1120=? 112^0=\text{?}

2

Step-by-step solution

We use the zero exponent rule.

X0=1 X^0=1 We obtain

1120=1 112^0=1 Therefore, the correct answer is option C.

3

Final Answer

1

Key Points to Remember

Essential concepts to master this topic
  • Zero Exponent Rule: Any non-zero number raised to the zero power equals 1
  • Technique: Apply a0=1 a^0 = 1 directly to get 1120=1 112^0 = 1
  • Check: Verify using division pattern: 1122÷1122=1120=1 112^2 ÷ 112^2 = 112^0 = 1

Common Mistakes

Avoid these frequent errors
  • Thinking zero exponent equals zero
    Don't confuse 1120 112^0 with 0×112=0 0 × 112 = 0 ! The zero is the exponent, not the base, so it follows the zero exponent rule. Always remember that any non-zero number to the zero power equals 1.

Practice Quiz

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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 division pattern: 1123÷1121=1122 112^3 ÷ 112^1 = 112^2 , 1122÷1121=1121 112^2 ÷ 112^1 = 112^1 , 1121÷1121=1120 112^1 ÷ 112^1 = 112^0 . Since any number divided by itself equals 1, we get 1120=1 112^0 = 1 !

Does this work for negative numbers too?

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Yes! The zero exponent rule works for any non-zero number. So (5)0=1 (-5)^0 = 1 and (112)0=1 (-112)^0 = 1 . The only exception is 00 0^0 , which is undefined.

What about 0^0?

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00 0^0 is undefined in most contexts because it leads to mathematical contradictions. Remember the zero exponent rule only applies to non-zero bases!

How is this different from 0 × 112?

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Completely different! 1120 112^0 means "112 raised to the zero power" which equals 1. But 0×112 0 × 112 means "zero times 112" which equals 0. The position of zero matters!

Can I use a calculator to check this?

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Absolutely! Most calculators have an exponent button (usually ^ or **). Type 112^0 and you'll get 1, confirming the zero exponent rule works perfectly.

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