Integrated Math 2 / Unit 1: Exponents and Radicals
1.2 Zero and Negative Exponents
Notes
Exponents can be zero or negative, and they follow the same rules.
- Zero exponent: $a^0 = 1$ for any $a \neq 0$.
- Negative exponent: $\displaystyle a^{-n} = \frac{1}{a^n}$. A negative exponent means "reciprocal", not a negative number.
- Move a factor with a negative exponent across the fraction bar to make the exponent positive.
- Example: $\displaystyle \frac{3x^{-2}}{y^{-1}} = \frac{3y}{x^2}$.
Practice
Simplify $7x^0$ for $x \neq 0$.
Only $x$ is raised to the zero power, so $x^0 = 1$ and $7 \cdot 1 = 7$.
What is $2^{-3}$?
$\displaystyle 2^{-3} = \frac{1}{2^3} = \frac{1}{8}$. The negative exponent does not make the answer negative.
Write $\displaystyle \frac{3x^{-2}}{y^{-1}}$ with positive exponents.
$x^{-2}$ moves to the denominator and $y^{-1}$ moves to the numerator. The 3 stays put.
Ready for more? Take the Unit 1 test.