MATH1000 Section1.2

1. Math 1000
Stuart Jones
Section 1.2 Exponents and Radicals

2. Math 1000
Stuart Jones
What is an exponent?

3. Math 1000
Stuart Jones
What is an exponent?
Example 1: −24

4. Math 1000
Stuart Jones
What is an exponent?
Example 1: −24
Example 2: (−2)4

5. Math 1000
Stuart Jones
What is an exponent?
Example 1: −24
Example 2: (−2)4
Example 3: (1/2)3 · (−3)2

6. Math 1000
Stuart Jones
Rules for Exponents
1 xa · xb = xa+b
2 xa
xb = xa−b
3 (xa)b = xab
4 1a = 1, for all a
5 x0 = 1, for all x = 0
6 x−1 = 1
x

7. Math 1000
Stuart Jones
Simplify 4x3(−2x2)(4x5)

8. Math 1000
Stuart Jones
Simplify 4x3(−2x2)(4x5)
Answer: − 32x10

9. Math 1000
Stuart Jones
Simplify (6x2y4)(2xyz2)
−4xy2z

10. Math 1000
Stuart Jones
Simplify 3a4b−2c−5
2a−5b−6c5 · 4abc3
2a2b−3

11. Math 1000
Stuart Jones
Radicals

12. Math 1000
Stuart Jones
Radicals
16
25

13. Math 1000
Stuart Jones
Radicals
16
25
4
√
81

14. Math 1000
Stuart Jones
Radicals
16
25
4
√
81
5
√
−1024

15. Math 1000
Stuart Jones
Radicals
16
25
4
√
81
5
√
−1024
√
20

16. Math 1000
Stuart Jones
Radicals
16
25
4
√
81
5
√
−1024
√
20
√
54

17. Math 1000
Stuart Jones
Rational Exponents
Rational Exponents
n
√
x = x
1
n

18. Math 1000
Stuart Jones
Simplify a
1
3 a
4
3

19. Math 1000
Stuart Jones
Simplify (3ab2)
3
2

20. Math 1000
Stuart Jones
Simplify x3y
2
3 z− 3
2
x−3y− 1
3 z

21. Math 1000
Stuart Jones
Simplify 3
y4 · 2
y−3 ·
5
y−3
2

22. Math 1000
Stuart Jones
The Bottom Line
Pay attention when the base is negative, ie −36 vs (−3)6
0 and 1 are special exponents – know what they mean!
Multiplying like bases - add exponents. Divide like bases -
subtract exponents
Radicals distribute over fractions.
Negative exponent means reciprocal - ”flip it”
Variables change nothing – they are just like numbers!