Powers Review
Powers are calculated by multiplying the base by itself
the number of times indicated by the exponent. As multiplication is
to repeated addition, powers are to repeated multiplication.
power = base^{exponent} = base^exponent
Special names are used for exponent two and three.
base^{2}
=base x base = base^2 = base
squared
base^{3}
= base x base x base = base^3
= base cubed
Concept/Term 
Example(s) 
Definition/Explanation 
power

81 is the fourth power of 3, because: 3 x 3 x 3 x 3 = 81
3^{4} is another way of writing this power 
the answer from multiplying a number by itself one or more times. A power
has two parts:
base^{exponent }=
3^{4 }
and can be written/read in several ways:
 the fourth power of three
 three exponent four
 three to the fourth power

3^{2}
3^{3} 
Exponents 2 and 3 can also be written/read another way:
 3^{2} is read three squared
 3^{3} is read three cubed

base 
In 3^{4}
, the base is 3. 
the number being multiplied in a power 
exponent 
In 3^{4}
, the exponent is 4. 
the number of times a number is being multiplied by itself in a power 
coefficient 
In 5x^{2},
the coefficient is 5. 
the constant (number) multiplier of the variables in a term 
Exponential
Form (Power) 
Expanded
Form/Repeated Multiplication 
Standard
Form (Standard Name) 
3^{4} 
3 x 3
x 3 x 3 
81 
3^{3} 
3 x 3 x 3 
27 
3^{2} 
3 x 3 
9 
3^{1} 
3 
3 
3^{0} 
no expanded form 
1 
Note: The standard name of any nonzero
base with an exponent of zero is equal to 1. 