Algebra 1 / Unit 7: Exponents and Exponential Functions
7.2 Zero and Negative Exponents
Notes
- Zero exponent: $a^0 = 1$ for any $a \ne 0$.
- Negative exponent: $\displaystyle a^{-n} = \frac{1}{a^n}$. A negative exponent moves the factor across the fraction bar.
- Final answers usually use only positive exponents: $\displaystyle \frac{x^{-3}}{y^{-2}} = \frac{y^2}{x^3}$.
Practice
$5^0 =$
Any nonzero number to the 0 power is 1.
$2^{-3} =$
$\displaystyle \frac{1}{2^3}$.
Simplify $\displaystyle \frac{6x^2}{2x^5}$ with positive exponents.
$\displaystyle 3x^{2-5} = 3x^{-3} = \frac{3}{x^3}$.
Ready for more? Take the Unit 7 test.