<p>Exponents and Exponential Notation a x a x a x a x a = a5</p><p>Exponential notation was developed by Rene Descartes in order to simplify mathematical equations relating to measurement.</p><p>In the example above the “a” is the base (the factor). The exponent (5) represents the number of equal factors in the expression. </p><p>Ex: X x X x X x X = X4</p><p>Ex: 2m2 = 2 x m x m ex: (2m)2 = 2m x 2m Multiplying and Dividing Exponents</p><p>Multiplying</p><p>When you have the same base when multiplying you can simply keep the base and add the exponents. ex: a5 x a3 = (a x a x a x a x a) x (a x a x a)</p><p>= a8 Another way of seeing this is: a5 x a3 = a(5+3) = a8 </p><p>Dividing</p><p>When you have the same base when dividing you can simply keep the base and subtract the exponents. ex: : a5 / a3 = a x a x a x a x a = a(5 - 3) a x a x a </p><p>= a2 Distributive Property</p><p>When multiplying an expression within brackets the factor multiplying affects every term within the brackets. ex: a(b + c – d) = ab + ac – ad</p><p>Exponents: Power of a Power</p><p>When you encounter the power of a power:</p><p>1) Keep the base 2) Multiply the exponents</p><p> ex: (am)n = amn </p><p>(22)2 = 24 Observe in expanded notation: (22)2 = (2 x 2) x (2 x 2) = 24 Distribution of Exponents</p><p>In general the power of a product is equal to the product of the powers. ex: (abcde)4 </p><p>= (abcde) x (abcde) x (abcde) x (abcde)</p><p>= (a x a x a x a) x (b x b x b x b) x (c x c x c x c) x (d x d x d x d) x (e x e x e x e)</p><p>= a4b4c4d4e4</p>