Laws
of
Exponents

Lesson 1: Laws of Exponents
Vocabulary
exponent
7 2
base
power

Lesson 1: Laws of Exponents
Power Exponent Base

Lesson 1: Laws of Exponents
Law 1: Product Law
aman = am+n
When multiplying two powers with the
same base, just add the exponents.

Lesson 1: Laws of Exponents
Law 2: Quotient Law
m
a n = am-n
a
When dividing two powers with the
same base, just subtract the exponents.

Lesson 1: Laws of Exponents
Law 2: Power Law
(am)n = amn
To simplify any power of power,
simply multiply the exponents.

Lesson 1: Laws of Exponents
Powers with different bases
anbn = (ab)n

Lesson 1: Laws of Exponents
Powers with different bases
n n
an =  a 
 
 
b b 
Dividing different bases can’t be simplified
unless the exponents are equal.

Lesson 1: Laws of Exponents
Zero exponents
a =1
0
A nonzero base raised to a zero exponent
Is equal to one.

Lesson 1: Laws of Exponents
Negative exponents
 1
a-n =  
 n
a 
A nonzero base raised to a negative exponent
is equal to the reciprocal of the base raised
to the positive exponent.

Lesson 1: Laws of Exponents
Simplifying Powers
A power is in its simplest form when the laws and
definitions of exponents cannot be applied
further to simplify it.
Example: 4-3 not in simplest form
1
simplest form
64

Lesson 1: Laws of Exponents
Simplifying an Exponential Expression
Exponential expressions are algebraic
expressions which contain exponents.
An algebraic expression is in simplest form
when it is written with only positive exponents. If
The expression is a fraction in simplest form, the
only common factor of the numerator and
denominator is 1.

Lesson 1: Laws of Exponents
Evaluating an Exponential Expression
To evaluate means to substitute the given
value/s to the variable/s of the expression
and simplifying the expression.