Solve for 7^0: Calculating a Number Raised to Zero Power

Zero Exponent Rule with Non-Zero Base

Solve the following problem:

70= 7^0=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's keep it simple.
00:08 Remember, any number to the power of zero equals one.
00:13 We'll use this in our exercise.
00:16 And that solves the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
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Understand the problem

Solve the following problem:

70= 7^0=

2

Step-by-step solution

To solve the problem of finding 70 7^0 , we will follow these steps:

  • Step 1: Identify the general rule for exponents with zero.

  • Step 2: Apply the rule to the given problem.

  • Step 3: Consider the provided answer choices and select the correct one.

Now, let's work through each step:

Step 1: A fundamental rule in exponents is that any non-zero number raised to the power of zero is equal to one. This can be expressed as: a0=1 a^0 = 1 where a a is not zero.

Step 2: Apply this rule to the problem: Since we have 70 7^0 , and 7 7 is certainly a non-zero number, the expression evaluates to 1. Therefore, 70=1 7^0 = 1 .

Therefore, the solution to the problem is 70=1 7^0 = 1 , which corresponds to choice 2.

3

Final Answer

1 1

Key Points to Remember

Essential concepts to master this topic
  • Rule: Any non-zero number raised to power zero equals 1
  • Technique: Apply a0=1 a^0 = 1 where a ≠ 0, so 70=1 7^0 = 1
  • Check: Verify that 7 is non-zero, then confidently state 70=1 7^0 = 1

Common Mistakes

Avoid these frequent errors
  • Thinking zero exponent makes the answer zero
    Don't assume 70=0 7^0 = 0 because of the zero exponent = completely wrong answer! The zero in the exponent doesn't make the result zero. Always remember that any non-zero base raised to the zero power 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 zero power equal 1?

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This comes from the pattern of exponents! Look at this sequence: 73=343 7^3 = 343 , 72=49 7^2 = 49 , 71=7 7^1 = 7 . Each time we decrease the exponent by 1, we divide by 7. So 70=7÷7=1 7^0 = 7 ÷ 7 = 1 !

What happens with 00 0^0 ?

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Great question! 00 0^0 is actually undefined in most contexts. The rule a0=1 a^0 = 1 only works when the base is not zero. Since 7 ≠ 0, we can safely say 70=1 7^0 = 1 .

Does this work with negative numbers too?

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Yes! Any non-zero number raised to the zero power equals 1. So (5)0=1 (-5)^0 = 1 , (12)0=1 (\frac{1}{2})^0 = 1 , and (π)0=1 (\pi)^0 = 1 .

How is this different from 71 7^1 ?

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71=7 7^1 = 7 (the base itself) while 70=1 7^0 = 1 (always 1 for non-zero bases). The exponent determines the result, not the base when the exponent is 0!

Can I just memorize this rule?

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Yes, but understanding helps too! Memorize 'non-zero base to zero power equals 1' but also remember the pattern: as exponents decrease, we keep dividing by the base until we reach 1.

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