The expression 4x is shorthand for x + x + x + x, that is x added to itself four times. Likewise x4 is shorthand for x · x · x · x —x multiplied by itself four times. In x4, x is called the base and 4 is the power or exponent. We say ‘‘x to the fourth power’’ or simply ‘‘x to the fourth’’. There are many useful exponent properties. For the rest of the chapter, a is a nonzero number.
Property 1 anam
= am+n
When multiplying two powers whose
bases are the same, add the exponents.
Examples
23
· 24 = (2
· 2 · 2)(2
· 2 · 2 · 2) =
27
x9 · x3 = x12
Property 2 
When dividing two powers whose bases
are the same, subtract the denominator’s power from the numerator’s power.
Examples
Property 3 (an)m
= anm
If you have a quantity raised to a
power then raised to another power, multiply the exponents.
Examples
(53)2 = (5 · 5 · 5) = (5 · 5 · 5) (5 · 5 · 5) = 56
Be careful,
Properties 1 and 3 are easily confused.
Property 4 a0
= 1
Any nonzero number raised to the zero
power is one. We will see that this is true by Property 2 and the fact that any nonzero number over
itself is one.
Practice
Rewrite using a single exponent.
Solutions
These properties also work with
algebraic expressions.
Practice
Solutions
Sumber
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