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If a^0 = 1 for any non-zero number a, which of the following is true?

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Question: If a^0 = 1 for any non-zero number a, which of the following is true?

Options:

  1. 0^0 is also equal to 1.
  2. 1^0 is equal to 0.
  3. Any number raised to the power of 0 is undefined.
  4. Only positive numbers can be raised to the power of 0.

Correct Answer: 0^0 is also equal to 1.

Solution: 

By convention, 0^0 is often defined as 1 in combinatorics, although it can be considered indeterminate in other contexts.

If a^0 = 1 for any non-zero number a, which of the following is true?

Practice Questions

Q1
If a^0 = 1 for any non-zero number a, which of the following is true?
  1. 0^0 is also equal to 1.
  2. 1^0 is equal to 0.
  3. Any number raised to the power of 0 is undefined.
  4. Only positive numbers can be raised to the power of 0.

Questions & Step-by-Step Solutions

If a^0 = 1 for any non-zero number a, which of the following is true?
  • Step 1: Understand that 'a^0' means 'a raised to the power of 0'.
  • Step 2: Remember that for any non-zero number 'a', 'a^0' equals 1.
  • Step 3: Recognize that this rule applies to all non-zero numbers.
  • Step 4: Consider the case of '0^0'.
  • Step 5: Know that '0^0' is often defined as 1 in combinatorics, but it can be seen as indeterminate in other areas of math.
  • Step 6: Conclude that while 'a^0 = 1' is true for non-zero 'a', '0^0' is a special case.
  • Exponentiation – Understanding the properties of exponents, particularly the rule that any non-zero number raised to the power of zero equals one.
  • Indeterminate Forms – Recognizing that 0^0 is often treated as an indeterminate form in mathematics, though it is defined as 1 in certain contexts like combinatorics.
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