Lesson 1-4: Zero and Negative Exponents

Property

For any non-zero number $a$, a number raised to the power of zero is equal to 1.

Examples

Property

A negative exponent indicates the reciprocal of the power with the positive exponent. This means a factor can be moved from the numerator to the denominator (or vice versa) of a fraction by changing the sign of its exponent.

Examples

• To write without a negative exponent: $5^{-3} = \frac{1}{5^3} = \frac{1}{125}$.
• For a fraction raised to a negative power, take the reciprocal of the fraction and make the exponent positive: $(\frac{2}{3})^{-4} = (\frac{3}{2})^4 = \frac{81}{16}$.
• To rewrite a fraction using a negative exponent: $\frac{5}{y^2} = 5y^{-2}$.

Explanation

A negative exponent tells you to flip the base to the other side of the fraction bar. An expression like $x^{-n}$ in the numerator becomes $\frac{1}{x^n}$ in the denominator. It's a way to write reciprocals, not to make the number negative.

Property

For any positive number $n$, zero raised to that power is zero ($0^n = 0$). However, zero raised to the power of zero is undefined:

Examples