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)
axaxa
= 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