Patterns with Exponents
Remember that a positive integer exponent means repeated multiplication.
For example,
8
2222
3
=
⋅⋅=
Notice that the order is important: 23 is different from 32. Let’s see what can
happen when we perform certain operations on powers.
Example 1: What is the result of multiplying two powers of the same base?
( ) ( )
43
43
2
222222222
+
=
⋅⋅⋅⋅⋅⋅=⋅
To multiply powers of the same base, you can add the exponents.
Example 2: What is the result of dividing two powers of the same base?
58
5
8
2
22222
22222222
2
2
−
=
⋅⋅⋅⋅
⋅⋅⋅⋅⋅⋅⋅
=
To divide powers of the same base, you can subtract the exponents.
Example 3: What is the result of raising a power to another power?
( )
( )( )( )
35
3
5
2
2222222222222222
⋅
=
⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅=
To raise a power to another power, you can multiply the exponents.
