Sum exponents when multiplying $x^a * x^b = x^{a + b}$ Subtract exponents when dividing $\frac{x^a}{x^b} = x^{a - b} = \frac{1}{x^{b - a}}$ Multiply exponents when exponentiating $(x^a)^b = x^{ab}$. Distribute exponents $(xy)^a = x^a y^a$ Any number to the power of $0$ is $1$. Any number to a negative exponent is the same as 1 over that number to the positive exponent. The root of a number is the same as raising the number to one over the root.