Why are 4^0 and (-4)^0 is equal to 1,while -4^0 is equal to -1

Answer

4^0 and (-4)^0 both have positive bases, so they equal 1 by the rule stated in step 1. However, -4^0 first requires us to perform the operation inside the parentheses, which makes it -1. Then, we raise -1 to the power of 0, which equals -1. Thus, -4^0 is equal to -1.

Q: What is the rule for raising any number to the 0th power? A: Any number raised to the 0th power is equal to 1.
Q: What is the order of operations when there is a negative sign in an exponent? A: When there is a negative sign in an exponent, we perform the operation inside the parentheses first.
Q: What is the order of operations when there is a negative sign and an exponent of 0? A: When there is a negative sign and an exponent of 0, we first perform the operation inside the parentheses, then raise the result to the power of 0.