Understanding Zero and Negative Exponents

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, $x^0 = 1$ 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, $a^{-n} = \frac{1}{a^n}$. This means if you see $x^{-2}$, it equals $\frac{1}{x^2}$. 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! $-3^0 = -1$ 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 $\frac{s^0}{r^{-2}}$ becomes $\frac{1}{(-3)^{-2}}$, which equals $\frac{1}{1/9} = 9$. With practice, these patterns will become second nature!