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Pre-Algebra
Chapter 4 Study Guide
Name _______________
Exponents show repeated multiplication.
x3 = x • x • x
25 = 2 • 2 • 2 • 2 • 2
A negative sign in front of a term means
“the opposite of” -(4)2 = - 16
If the negative sign is inside the parenthesis, as in
(-4)2 , it means (-4)(-4) = 16
The order of operations states that you must work inside the
parenthesis before raising to a power. Remember PEMDAS
25 + 2(1 + 5)2
25 + 2(6)2 = 25 + 2(36)
25 + 72 = 97
3(6-4)3
3(2)3 = 3(8) = 24
Evaluate (x + y)3 for x = 3 and y = -6
(3 + -6)3 = (-3)3 = -27
Use prime factorization to find the greatest common factor (GCF) of
two numbers. Remember that factors are small. With variables, use the
smallest exponent of each variable that both terms have in common.
56 = 2 • 2• 2 • 7
42 = 2 • 3 • 7
Their GCF is 2 • 7 which is 14.
Find the GCF of 64 and 48. (Use the cake method)
16
Find the GCF of 28xy7 and 32x2y4 (Use the cake method for the
coefficients)
4xy4
Two numbers are relatively prime if their GCF is 1. The numbers by
themselves may not be prime, but compared to each other, they have
no factors in common. All numbers have 1 as a factor.
You can find equivalent fractions by multiplying or dividing the
numerator and denominator by the same nonzero factor. A fraction is
in simplest form when the numerator and denominator have no common
factors other than 1.
p
2p
divide the numerator and denominator
by the common factor, p
p =1
2p 2
Simplify
3ab2
12ac
b2
4c
42 + 2(-3)
5
28
35
16 + -6
5
10
5
4
5
2
1
x5
x5
6
18x0
3
Evaluate each expression for a = -4 and b = -3
b
a
3
4
b–a
a–b
-3 - -4
-4 - -3
-1
b2
a2
9
16
To multiply numbers with the same base, add the exponents. To divide
numbers with the same base, subtract the exponents. To find a power
of a power, multiply the exponents.
x5 • x2 • y4 • y-2 = x7y2
38
35
33
x6y5
x3y3
x3y2
(23)4 = 212
(x5)6 x30
14rs3
8r2st
7s2
4rt
Scientific notation is the product of two factors, a decimal greater
than or equal to 1, and a power of 10. Big numbers have positive
exponents, and small numbers have negative exponents.
458,000,000 = 4.58 x 108
0.0000007 = 7.0 x 10-7
Write in scientific notation
0.0004531
4.531 x 10-4
72,430,000
7.243 x 107
207,500
2.075 x 105
.00008524
8.524 x 10-5
Write in standard notation
3.21 x 107
32,100,000
5.9 x 10-8
.000000059
7.423 x 108
742,300,000
9.01 x 10-2
.0901