The document provides examples of arithmetic operations involving exponents, including addition, subtraction, multiplication, and division of exponential expressions. It gives examples of applying the product rule, power of a product rule, and simplifying expressions using laws of exponents. There are over a dozen problems provided to work through applying these exponent rules and properties.

1. Add the following.
• 1) (−7) + 9 2) (−47) + 30
• 3) (−8) + (−1) 4) 49 + (−27)
• 5) (−1) + 5 6) (−29) + 9
• 7) (−6) + 12 8) 43 + (−1)
• 8) (−8) + (−5) 9) 10 + (−2) + 1
• 10) 11 + (−2) 11) (−2) + 11 + 4
• 13) 49 + (−15) 14) 12 + 7 + (−4)

2. Multiply the following
1.(-2)(3)
2.(7)(-6)
3.(5)(-2)(-3)
4.(-1)(-3)(-3)
5.(9)(-7)
6.(-5)(-6)
7.(-8)(-7)

3. Identify the base and exponents of
the following expressions
1) 34
2) -52
3) (-6)4
4) 2x4y5
5) (5a2)5

4. Express in Exponential Form
1) 4.4.4.4.f.f
2) 7.u
3) 7.x.y.7.x.y.7.x.y
4) m.m.m.m.n.n.n
5) 5.5.x.x.x.y.y.y.z.z.z

5. Explore It...
Change the bars as directed:
• m (purple) to 2
• n (yellow) to 3
• x (red) to 4
x x
m n

6. Explore It...
Change the bars as directed:
• m (purple) to 2
• n (yellow) to 3
• x (red) to 4
4 4
2 3

7. Complete Me
Exponential
Form
(42)(43)
Expanded
Form
(___)2 + 3 (4)(4)__ __ __
(4)____

8. Change the bars as directed:
• m (purple) to 4
• n (yellow) to 3
• x (red) to 2
x
m n

9. Change the bars as directed:
• m (purple) to 4
• n (yellow) to 3
• x (red) to 2
2
4 3

10. Complete Me
Exponential Form
(24)3
Expanded Form
(___)(4)(3) (2)(2)__ __ __
(2)____

11. Laws of Exponent
•Product Law of
Exponents
•Power of a Product

12. Product Rule
• For any number a and all
integers m and n:
am . an = a m + n
1) x3.x4
2) x5.x2.y2.y3
3) (2x3)(-3x2)
4) (-3xy5)(-4x4y7z2)
5) (9a3b3c2)(-2a2b3c4)
x7
x7y5
-6x5
12x5y12z2
-18a5b6c6

13. Power of a Product
• For any number a and all integers m and n:
(am)n = a (m)( n)
1. (x2)3
2. (x3y2)4
3. (-2x5yz3)3
4. (3m4n2)4
5. (-5a5b4c6)2
x6
x12y8
-8x15y3z9
- 81m16n8
25a10b8c12

14. Simplify the following
expressions.
1. 43.410.45
2. (5x4)(6x3)
3. (3y5)(-2y)4
4. (2x9y4)(24x5y3)
5. (-x2y3)4
418
30x7
48y9
48x14y7
x8y12

15. 6.(4-3)(45)
7. (a)(a10)
8.(x8)4
9. (2a2)4
10. (5m-1n2)(-3m3n)
42
a11
x32
16a8
-15m2n3