Exponent Rules And other mysteries of the universe.

Negative Exponents X -1 = The inverse of X = X -2 = The inverse of X 2 = X -3 = The inverse of X 3 = This pattern continues for all exponents. 1 X 1 X2X2 1 X3X3

The Zero power X o = 1 ; X ≠ 0 For any value we allow X to be, when it is raised to the zero power it is equal to 1. The only exception is zero to the zero power. This value is undefined. (no solution)

Multiplying variables with exponents Rule: X a X b = X a+b We can see that X 2 is X times itself twice and X 3 is X times itself three times and when we multiply them together we get X times itself five times. If we have X 2 X 3 = (X X) (X X X) So X 2 X 3 = X 2+3 = X 5.

Distribution of exponents Rule: (X a ) b = X a b Let n be any number: (nX a ) b = n b X a b Caution (n + X a ) b ≠ n b + X a b The correct distribution here requires the FOIL method which we will learn when we begin algebra.

Division of variables with exponents XaXa = X a- b XbXb X5X5 = X X X X X = X2X2 X3X3 X X X 1 \\ \ \ \ \

Examples Answer using only positive exponents X2 X3X2 X3 = X7X7 X 2+3 = X7X7 X 5-7 = X - 2 = 1 X2X2 (3X 2 ) 3 = 27X 6 = 3 3 X 2 3