Introduction to Exponents

• Definition: Let b represent a real number and n a positive integer. Then …

...nb b b b b

b is called the base and n is called the exponent.

n factors of b

• Example 1

43

Base: 3

Exponent: 4

Result: 3 3 3 3 81

4 factors of 3

• When we expand an exponential expression we say that we are evaluating the exponential expression

26

• Example 2

Evaluate:

Important note: the exponent only applies to what immediately precedes it, or the 6 in this case, but not the negative.

26 1 6 6 36

26

• Example 3

Evaluate:

Since this time the -6 is in parentheses, the exponent applies to both the 6 and the negative.

26 6 6 36

32

• Example 4

Evaluate:

2 2 2 8 32

42

• Example 5

Evaluate:

2 2 2 2 16 42

42

• Example 6

Evaluate:

1 2 2 2 2 1642