Zero and Negative Exponents
When you see a number raised to the power of zero, the answer is always 1. It doesn't matter what the base number is (as long as it's not zero itself). For example, x0=1 and (−4.25)0=1. This rule makes calculations much simpler!
Negative exponents tell you to take the reciprocal of the base raised to the positive power. In other words, a−n=an1. This means if you see x−2, it equals x21. When working with fractions containing negative exponents, you can move terms with negative exponents to the opposite side of the fraction line.
Quick Tip: Be careful with negative signs! −30=−1 because the negative sign is outside the exponent, while (−3)0=1 because the entire number is being raised to the power.
When evaluating expressions with variables that have negative exponents, substitute the values first, then apply the rules. For example, when r=−3 and s=5, the expression r−2s0 becomes (−3)−21, which equals 1/91=9. With practice, these patterns will become second nature!