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?
0^0 is also equal to 1.
1^0 is equal to 0.
Any number raised to the power of 0 is undefined.
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.
