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Exponents and Exponential Expressions
Multiplying and Simplifying Expressions Containing Powers of Monomials
Sections: 7-3 and 7-4
SOL: A.2.a
Dividing and Simplifying Expressions Containing Negative Exponents
Sections: 7-1 and 7-5
SOL: A.2.a
Multiplying Powers With the Same Base
Vocabulary:
Base:
Exponent:
Property:
Algebra:
Examples:
What is each expression written using each base only once?
What is the simplified for of each expression?
Using Scientific Notation
Working Backwards:
Form K
Rewrite each expression using each base only once.
1. 107 • 102
2. 63 • 61 • 68
3. 78 • 71 • 75
4. 46 • 43 • 44
5. 122 • 129 • 1212
6. 34 • 35 • 36
Simplify each expression.
7. t3t9
8. 3y8 • 5y5
9. (7a1)(3a5)
10. 3j6 • 12j
11. (m)(m4)(m2)
12. (8h3)(5h4)
13. x3y1 • xy • x2y2
14. (3f 2g3)(2fg)(7f 3 g2)
Simplify each expression. Write each answer in scientific notation.
15. (2  106)(4  109)
16. (3  108)(3  105)
17. (7  1011)(8  104)
18. (6  107)(6  104)
Complete each equation.
23.
35  3  310
24. 83 85  8
25.
w3  w8=w
26.
a 5  a =a 4 =a3
Simplify each expression. Write each answer in scientific notation.
27. (9  1014)(6  1012)
28. (5  104)(0.6  1010)
29. (0.2  1022)(0.9  1030)
30. (0.25  107)(12  1015)
More Multiplication Properties of Exponents
Property:
Algebra:
Examples:
Simplifying a Power to a Power
Property:
Algebra:
Examples:
Simplifying a Product Raised to a Power
Book:
Form K
Simplify each expression.
1. (v4)2
2. (a5)7
3. (n4)6
4. h(h3)10
5. (x3)4y3
6. (3q)5
7. (a4)6(b5)2
8. (m2)8(n0)4
9. (2t3)4
10. (5k9)3
11. (3s4)3s2
12. (bc3)5
13. (mnp)0
14. (f 2 g3)(fg4)1
15. a(a3b4)2b3
16. (5x2)2(y7z5)4
17. c10(c4d3)4d3
18.
7t11u3(4t9)2u5
Simplify. Write each answer in scientific notation.
19. (4  103)2
20. (7  108)4
22. (5  107)3
23. (2.5  1010)2
21. (1.4 
108)3
24. (4.8 
104)2
25. The radius of a cylinder is 2.9  105 in. The height of the cylinder is 3.8  104
in. What is the volume of the cylinder? (Hint: V = r2h)
26. The side length of a square is 9.5  102 cm. What is the area of the square?
Zero and Negative Properties
Property:
Algebra:
Examples:
Property:
Algebra:
Examples:
What is the value of
x=2 and y= - 3?
for
What is the value of
a= - 2 and b= 4?
for
Form K
Simplify each expression.
1. 370
3.
5
5 2
2. 34
4.
3
6 1
5. (5)2
6. 1121
7. 110
8. (7n)2
9. (15p)0
3
10.  
5
11. 4x3y0
8m 2
12.
4n 1
13.
6a 2 (bc) 2
d 4
2
 5s 

 6t 
2
14. 
15. 42h4j3
16. (6yz)2x0
10 fg -5 h0
17.
h-2
18.
6t -1
11 uv  w4
Evaluate each expression for x = 2, y = 4, and z = 2.
21. 2xy2z2
22. 6x3z0
-3
Book
Division Properties
Property:
Algebra:
Dividing Powers with the same base
and m and n are integers
Examples:
Property:
Algebra:
Examples:
Raising a Quotient to a Power
Book: