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Chapter 4
PreTest
Leave your answer in exponent form.
1.
(36)(34)
36 + 4
310
Product Rule.
Leave your answer in exponent form.
2.
214
26
214 – 6
28
Quotient Rule.
Leave your answer in exponent form.
3.
5
3
(2 )
23 • 5
215
Power Rules.
Simplify. Use positive exponents.
4.
(-2 x y3 )( 5x3 y5 )
-10 x4 y8
Multiply.
Product Rule.
Simplify. Use positive exponents.
5.
-20x7y4
12x12y3
-5y
3 x5
Simplify.
Quotient Rules.
Simplify. Use positive exponents.
6.
2
5
3
( 3x y )
9x6 y10
Evaluate.
Power Rules.
Simplify. Use positive exponents.
7.
(
5x3y2 5
3 z5
)
55 x15 y10
35 z25
or
Power Rules.
Evaluate.
3125 x15 y10
243 z25
Simplify. Use positive exponents.
8.
15x5y10
10x12y10
3
2x7
Simplify.
Quotient Rules.
Simplify. Use positive exponents.
9.
3-3
1
33
1
27
Negative exponents.
Evaluate.
Simplify. Use positive exponents.
10.
7x-3y-4 z
7z
x3 y4
Negative exponents.
Simplify. Use positive exponents.
11.
3x-3 y-2
z-5
3 z5
x3y2
Negative exponents.
12. Write in scientific notation.
104,000,000
104000000.
1.04 x 108
Count the number of places to move.
Positive 8 is the exponent.
13. Write in decimal notation.
1.9 x 10-3
00019
.
0.0019
The exponent is negative 3.
Move the decimal point left 3 places.
14. Multiply and write in scientific notation:
(6.4 x 103)(3.8 x 106)
24.32 x 109
Multiply the numbers.
Use the product rule.
14. Multiply and write in scientific notation:
(6.4 x 103)(3.8 x 106)
24.32 x 109
2.432 x 101 x 109
2.432 x 1010
Write in scientific notation.
Use the product rule.
15. Add.
(4x2 – 5x + 2) + (6x2 – 7x – 5)
4x2 – 5x + 2 + 6x2 – 7x – 5
10x2 – 12x – 3
Remove both parentheses. Distribute + 1 to
each term in the second parentheses.
Combine like terms.
16. Subtract.
(2x2 – x + 3) – (4x2 + 5x – 3)
2x2 – x + 3 – 4x2 – 5x + 3
-2x2
– 6x + 6
Remove both parentheses. Distribute – 1 to
each term in the second parentheses.
Combine like terms.
17. Multiply.
-3 x3( 3x3
-9x6
Distribute.
+ 2x2 – 5)
– 6x5 + 15x3
18. Multiply.
-3x2y2(
-15x4 y5
Distribute.
5x2y3 – 6xy4 + 5 )
+ 18x3 y6 – 15x2 y2
19. Multiply.
(4x – y)(6x + 2y)
24x2 + 8xy – 6xy – 2y2
24x2 + 2xy – 2y2
Use FOIL to multiply.
Combine like terms.
Outer
First
Last
Inner
20. Multiply.
(4x – 5)( 4x + 5)
(4x)2 – (5)2
16x2 – 25
Special Case (a + b)(a – b) = a2 – b2
Square the first term.
Subtract the square of the second term.
21. Multiply.
(2x – 3y)2
(2x)2 – 2(2x)(3y) + (-3y)2
4x2 – 12xy + 9y2
Special Case (a – b)2 = a2 – 2ab + b2
Square the first term.
Subtract 2 times the first and second terms.
Add the square of the second term.
22. Multiply.
(2x + 5y2)( 2x4 – 4y3)
4x5 – 8xy3 + 10x4y2 – 20y5
Use FOIL to multiply.
No like terms.
Last
Inner
Outer
First
23. Multiply.
( 3x – 4)( x2 – 2x + 5 )
3x3 – 6x2 + 15x – 4x2 + 8x – 20
3x3 – 10x2 + 23x – 20
Multiply each term.
Combine.
24. Divide.
(16x4 – 24x3 – 4x2) ÷ 4x2
16x4
4x2
–
24x3
4x2
–
4x2
4x2
4 x2 – 6 x – 1
Write as separate fractions.
Simplify each.
25. Divide.
(3x3 – 13x2 + 27x – 20) ÷ (3x – 4)
x2 – 3x + 5
3x3 -9x2 15x
3x – 4 ) 3x3 – 13x2 + 27x – 20
3x 3x 3x
–( 3x3 – 4x2 )
-9x2 + 27x
2 + 12x )
–(
-9x
Write as long division.
15x – 20
Divide first terms.
–(15x – 20 )
Multiply.
Subtract.
Bring down next term.
x2 – 3x + 5
Chapter 4
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