Download Negative Exponents

Math 10C
Real Numbers: Lesson #8
Negative Exponents
Objective: By the end of this lesson, you will be able to:
- Explain the meaning of a negative exponent, using patterns
- Evaluate a power that has a negative exponent
Warm-Up:
 How do you find a reciprocal?


Write the reciprocal of the following numbers:
2
i)
ii) 10
5
iii) 
9
4
What do you get when you multiply a number by its reciprocal? (If you don’t know, try it
with the three examples above.)
Exponents don’t have to be positive; they can also be negative.
But what does a negative exponent mean?
Let’s look at the following pattern to see how to evaluate negative exponents:
53  ______
5 2  ______
51  ______
5 0  ______

How does 5 3 compare to 5 3 ?
5 1  ______
5 2  ______
5 3  ______
We can also show this rule for negative exponents using exponent laws:
Complete the following:
 By expanding out according to the definition of exponents:
34  36 



 This means that:

 Using exponent laws:
4
6

3 3 

Math 10C
Real Numbers: Lesson #8
Negative Exponent Law:
To evaluate powers with negative exponents, take the _________________ of the base
and make the exponent ________________.
x
n

a
and  
b
n

*Important:
e.g. 1) Rewrite the following with a positive exponent, then evaluate:
a) 2
4
b)  
5
5
2
What happens if you have a negative exponent in the denominator? Let’s see what happens with
3
.
4 3
The Long Way:
The Shortcut:
e.g. 2) Simplify
385
using the shortcut above.
55 y 2
We can also have negative fraction exponents. Follow the same rule to make the exponent
positive, then use the rule we learned last class to write the power as a radical.
* Remember: With a negative exponent, take the reciprocal of the _________, not the
_________________. NEVER EVER flip the __________________.
e.g. 3) Rewrite each of the following with a positive exponent, as a radical, and then evaluate:
 9 
a)  
 49 

1
2
Math 10C
Real Numbers: Lesson #8
b) 16

3
4
27
c)   
 8 

5
3
e.g. 4) Paleontologists use measurements from fossilized dinosaur tracks
to estimate the speed at which the dinosaur travelled. The formula
5
3

7
6
v  0.155s f gives the approximate speed of the dinosaur in
metres per second, where s is the distance between successive
footprints of the same foot, and f is the foot length. Use the
measurements in the diagram to estimate the speed of the dinosaur
to the nearest tenth.
Assignment:
p. 233-234 #1, 5-9, 11-13, 15-16, 19
0.3 m
1.5 m