1. Negative Exponents Notes

2. What is an Exponent? x4 = x ● x ● x ● x 26 = 2 ● 2 ● 2 ● 2 ● 2 ● 2
An exponent means that you multiply the base by itself that many times.
For example
x4 = x
● x
● x
● x
26 = 2
● 2
● 2
● 2
● 2
● 2
= 64

3. Vocabulary
Power – a number produced by raising a base to an exponent. (the term 27 is called a power.)
Exponential form – a number written with a base and an exponent. (23)
Exponent – the number that indicates how many times the base is used as a factor. (27)
Base – when a number is being raised to a power, the number being used as a factor. (27)

4. Parts of a Power 2 4
exponent
base
Say: “2 to the fourth power”
power

5. The Invisible Exponent
When an expression does not have a visible exponent its exponent is understood to be 1.

6. Zero Exponent
When anything, except 0, is raised to the zero power it is 1.
For example
( if a ≠ 0)
( if x ≠ 0)

7. Negative exponents
An exponent that is negative is not fully simplified. To simplify a negative exponent, take the reciprocal of the entire power. Leave the base and exponent the same.
For example:

8. Negative Exponents
The negative exponent basically flips the part with the negative exponent to the other half of the fraction.

9. You simplify

10. Mixed Practice