Exponents and Exponential Notation

Exponents and Exponential Notation a x a x a x a x a = a5

Exponential notation was developed by Rene Descartes in order to simplify mathematical equations relating to measurement.

In the example above the “a” is the base (the factor). The exponent (5) represents the number of equal factors in the expression.

Ex: X x X x X x X = X4

Ex: 2m2 = 2 x m x m ex: (2m)2 = 2m x 2m Multiplying and Dividing Exponents

Multiplying

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)

= a8 Another way of seeing this is: a5 x a3 = a(5+3) = a8

Dividing

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

= a2 Distributive Property

When multiplying an expression within brackets the factor multiplying affects every term within the brackets. ex: a(b + c – d) = ab + ac – ad

Exponents: Power of a Power

When you encounter the power of a power:

1) Keep the base 2) Multiply the exponents

ex: (am)n = amn

(22)2 = 24 Observe in expanded notation: (22)2 = (2 x 2) x (2 x 2) = 24 Distribution of Exponents

In general the power of a product is equal to the product of the powers. ex: (abcde)4

= (abcde) x (abcde) x (abcde) x (abcde)

= (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)

= a4b4c4d4e4