1. Bell Ringer Solve. 1. 6x – 8 = -4x + 22
2x = 30
x = 15
2. -3(x – 6)= 3 -3x + 18 = 3 – 18 – 18 -3x = x = 5

2. Homework
1296
-1296
1/27
4096 1
1/125
-128 16 80
512
3/16 x3 y4
15x12
1/c9 n4
4x6y5
7y2/x3 3
1728 2x
2x2
-4/y2
5y/x2
2y2/x5
3x7/y2
6x2/y3z3

3. Laws of Exponents, Pt. I Review!
Zero Exponent Property Negative Exponent Property Product of Powers Quotient of Powers

4. Laws of Exponents, Pt. 1 x0 = 1 30 = 1 120 = 1 x-1 = 5-3 = 3x2y-3 = 1
Zero Exponent Property – Any number raised to the zero power is 1.
x0 = = = 1
Negative Exponent Property – Any number raised to a negative exponent is the reciprocal of the number.
x-1 = = x2y-3 = 1 x 1 53
3x2 y3

5. Laws of Exponents, Pt. 1 x2•x8 = x10 3x4•x-2 = 3x2 x6 x2 10x4y3 2x7y
Product of Powers – When multiplying numbers with the same bases, ADD the exponents. Quotient of Powers – When dividing numbers with the same bases, SUBTRACT the exponents.
x2•x8
= x10
3x4•x-2
= 3x2 x6 x2
10x4y3
2x7y
5y2 x3
= x4 =

6. Solve the problem in pieces.
Bonus!
Solve the problem in pieces.
30 x6 y2 z5
6 x3 y5 z8
5x3
y3z3 =
1. Whole numbers
2. x
3. y
4. z
10 x2 z6
15 x5 y3
2z6
3x3y3 =

7. 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

8. 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!

9. 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 =

10. 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

11. 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

12. ( ) ( ) 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 =

13. ( ) ( ) ( ) ( ) 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 = =

14. Basic Examples

15. Basic Examples

16. Basic Examples

17. More Difficult Examples

18. More Examples

19. More Examples