How to Express x to the Power of 0?

In mathematics, any non-zero number raised to the power of zero is equal to one. This can be expressed as:

x⁰ = 1 (for x ≠ 0)

This rule is a consequence of the laws of exponents. When we think about exponentiation, we often see it as repetitive multiplication. For instance:

• x³ = x × x × x
• x² = x × x
• x¹ = x
• x⁰ = ?

If we follow the pattern of decreasing the exponent by 1, we can rewrite x¹ as:

x¹ = x¹ × x⁰ / x¹

Here, we can see that if we divide x¹ by x¹, we get 1. Hence,:

x⁰ = 1

Remember that this rule only applies when x is not equal to zero. The expression 0⁰ is considered indeterminate in mathematics. So, as a general guideline, always consider x to be a non-zero number when using this exponent rule.