1. Bell Ringer Solve. 1. 5x + 18 = -3x – 14
8x = -32
x = -4
2. 7(x + 3)= 105 7x + 21 = x = x = 12

2. Quiz Results
Since there are still a few who haven’t taken the quiz, I’ll give out the results as soon as they do.
If you want to know your grade, log onto your Gradebook and check it yourself.
Otherwise, you’ll have to wait…
NO, I’m not digging through the papers to tell you your grade.

3. Exponents and Radicals
NCP 503: Work with numerical factors
NCP 505: Work with squares and square roots of numbers
NCP 506: Work problems involving positive integer exponents*
NCP 504: Work with scientific notation
NCP 507: Work with cubes and cube roots of numbers
NCP 604: Apply rules of exponents

4. Its read, “Three to the fourth power.”
Basic Terminology
Exponent 34
= 3•3•3•3 = 81
Its read, “Three to the fourth power.”
Base
The base is multiplied by itself the same number of times as the exponent calls for.

5. Important Examples -34 = –(3•3•3•3) = -81 (-3)4
= –(3•3•3•3) = -81
(-3)4
= (-3)•(-3)•(-3)•(-3) = 81
-33
= –(3•3•3) = -27
(-3)3
= (-3)•(-3)•(-3) = -27

6. x4 = x • x • x • x y3 = y • y • y Variable Expressions x4 y2
Evaluate each expression if x = 2 and y = 5
x4 y2
= (2•2•2•2)•(5•5)
= 400
3xy3
= 3•2•(5•5•5)
= 750

7. Laws of Exponents, Pt. I
Zero Exponent Property Negative Exponent Property Product of Powers Quotient of Powers

8. Zero Exponent Property
Any number or variable raised to the zero power is 1.
x0 = 1 y0 = 1 z0 = 1
70 = = = 1

9. Negative Exponent x-1 = y-1 = 5-1 = x-2 = 3-2 = = 5-3 = = 1 X 1 y 1 5
Any number raised to a negative exponent is the reciprocal of the number.
x-1 = y-1 = =
x-2 = = = = = 1 X 1 y 1 5 1 X2 1 32 1 9 1 53
1 .
125

10. Only x is raised to the -3 power!
Negative Exponent
3x-3 = 5y-2 = 2x-2 y2= 3-2 x4= 3 x3 5 y2
Only x is raised to the -3 power!
2y2 x2 x4 32 x4 9 =
Only x is on the bottom.

11. Product of Powers 53•52 = (5•5•5)•(5•5) = 55 x4•x3 = (x•x•x•x)•(x•x•x)
This property is used to combine 2 or more exponential expressions with the SAME base.
Multiplication NOT Addition!
53•52
= (5•5•5)•(5•5)
= 55
x4•x3
= (x•x•x•x)•(x•x•x)
= x7
If the bases are the same, add the exponent!

12. Product of powers also work with negative exponents!1
62•63 1 65 1
7776
6-2•6-3 = = = 1
x5•x7 1
x12
x-5•x-7 = =
n-3•n5 =
n-3+5 = n2

13. x6 x3 = x6-3 = x3 Quotient of Powers
This property is used when dividing two
or more exponential expressions with the same base. x6 x3
= x6-3
= x3
Subtract the exponents! (Top minus the bottom!)

14. 67 65 = 67-5 = 62 = 36 x3 x5 1 x2 = x3-5 = x-2 = OR x3 x5 x ∙ x ∙ x
Quotient of Powers 67 65
= 67-5
= 62
= 36 x3 x5 1 x2
= x3-5
= x-2 = OR x3 x5
x ∙ x ∙ x
x∙x∙x∙x∙x 1 x2 = =

15. Power of a Power Power of a Product Power of a Quotient
Laws of Exponents, Pt. II
Power of a Power
Power of a Product
Power of a Quotient

16. Power of a Power (63)4 = 63•63•63•63 = 612 (x5)3 = x5•x5•x5 = x15
This property is used to write an exponential expression as a single power of the base.
(63)4
= 63•63•63•63
= 612
(x5)3
= x5•x5•x5
= x15
When you have an exponent raised to an exponent, multiply the exponents!

17. Multiply the exponents!
Power of a Power
(54)8
= 532
Multiply the exponents!
(n3)4
= n12
(3-2)-3
= 36 1
x15
(x5)-3
= x-15 =

18. Power of a Product (xy)3 (2x)5 = x3y3 = 25 ∙ x5 = 32x5 (xyz)4
Power of a Product – Distribute the exponent on the outside of the parentheses to all of the terms inside of the parentheses.
(xy)3 (2x)5
= x3y3
= 25 ∙ x5
= 32x5
(xyz)4
= x4 y4 z4

19. Power of a Product (x3y2)3 (3x2)4 = x9y6 = 34 ∙ x8 = 81x8 (3xy)2
More examples…
(x3y2)3 (3x2)4
= x9y6
= 34 ∙ x8
= 81x8
(3xy)2
= 32 ∙ x2 ∙ y2
= 9x2y2

20. ( ) ( ) x x5 = y y5 Power of a Quotient
Power of a Quotient – Distribute the exponent on the outside of the parentheses to the numerator and the denominator of the fraction. ( ) ( ) x y 5 x5 y5 =

21. ( ) ( ) ( ) ( ) 2 x 23 x3 8 x3 = = 3 x2y 34 x8y4 81 x8y4 = =
Power of a Quotient
More examples… ( ) ( ) 2 x 3 23 x3 8 x3 = = ( ) ( 3
x2y ) 4 34
x8y4 81
x8y4 = =

22. Basic Examples

23. Basic Examples

24. Basic Examples

25. More Difficult Examples

26. More Examples

27. More Examples