3. Exponents are the mathematician's
shorthand.
In general, the format for using exponents is:
(base)exponent
where the exponent tells you how many of the base
are being multiplied together.
4. A Summary of Exponent Rules
1.
3.
4.
6.
8.
2.
Also Known as the power of a power rule.
5.
7.
16. Exponent Laws
1. p2 • p4 • q3 • q5 =
p 6q 8
Only exponents of the same bases can
be added.
Power of a Power Property
To find the power of a power, multiply the
exponents.
17. Exponents: Zero and One as Exponents
This is what the algebra text said about 0 as an exponent:
“When you have a 0 as an exponent, your answer will
always be 1.The only exception is 00, which is undefined”.
But this is incorrect. What they meant to say is:
When you have a 0 as an exponent, your answer will always
almost always be 1. The only exception One exception is
00, which is undefined. But there are others:
40 = 1
50000 = 1
- (-5)0 = -1
50 = 1
(-5)0 = 1
-(5)0 = -1
18. Negative and Zero Exponents
Take a look at the following problems and see if you
can find the pattern.
The expression a-n is the reciprocal of an
Examples:
19. Negative and Zero Exponents
Example 1
Example 2
Since 2/3 is in parenthesis, we must apply the power of a
quotient property and raise both the 2 and 3 to the negative
2 power. First take the reciprocal to get rid of the negative
exponent. Then raise (3/2) to the second power.
