Goat Math: Algebra I – Rules for Powers

When you multiply powers with the same base, you can add their exponents. When you divide powers with the same base, you can subtract their exponents, flipping sign, positive to negative, negative to positive, Exponents can be distributed onto numbers being multiplied or divided. Whenever you are adding or subtraction numbers together, and then raising to a power, you cannot distribute the power.

Raising any numbers to a power of zero (0) always give you one (1). Raising a number to a negative power equals 1 divided by that number to the positive power. Dividing 1 by a power is really the same as flipping the sign of the power going from positive to negative, or negative to positive. Taking a root is really the same as raising to a power, raising to the one-half power is the same thing as taking a square root. Raising number to one-third (1/3) power is the same thing as taking a cube root. The general rule for evaluating fractional powers; take the base, raise it to the power of the numerator and then take the denominator’s root. Raising a number to a fractional power is the same as raising it to the numerator and taking the denominator’s root. Roots can be distributed onto numbers being multiplied or divided. You cannot distribute roots onto addition and subtraction. Simplifying roots mean that getting smaller numbers under the root.