Question

In your own words, explain why x^0 (x to the power of zero) equals 1, if x ≠ 0. Include an example to support your explanation.

Answer 1

x^0 (x to the power of zero) equals 1 because any number raised to the power of zero is always equal to 1, as long as the number is not zero itself. This rule is derived from the properties of exponents.

Step-by-step explanation:

x^0 (x to the power of zero) equals 1 because any number raised to the power of zero is always equal to 1, as long as the number is not zero itself. This rule is derived from the properties of exponents. When we have x^0, we can think of it as the product of zero instances of x, which is essentially nothing to multiply. So, the answer is 1, the starting point for all multiplications.

For example, if we take the number 5 and raise it to the power of 0, we have 5^0. Using the rule, this is interpreted as the product of zero instances of 5. Since we have nothing to multiply, the answer is 1.