Math 152B
Intermediate Algebra
Spring 2013
Name______________________
Study Guide for Exam 1
The exam will be on Thursday, March 7th. You are allowed to use one 3" by 5" index card on the exam as well as a
scientific calculator.
For the exam you need to know how to do the following:
1. Evaluate radical expressions. Negative numbers under radicals with even indices are not real, but negative
numbers under radicals with odd indices are negative. We use absolute values to signify that variables are not
negative under even roots. 7.1
2. Change radical expressions to exponential expressions, and vice-versa, to evaluate or simplify. 7.2
n
1
n
n
n
n
n
a
a
* a a
* a
*
3. Apply the rules of exponents to rational and negative exponents. 7.2
m n
* product rule: x m x n x m n
* power rule: ( x )
* zero exponent rule: x 0
* quotient rule:
xm
xn
xm
n
a
m
n
or ( a )
m
a
m
n
xm n
* add/subtract with same base: x m
1
* negative exponent rule: x
n
ax
* expanded power rule:
by
a
m
n
m
am xm
bm y m
x n no rule!
1
1
and m x m
m
x
x
m
a
* fraction raised to negative exponent:
b
m
a
b
m
m
bm
am
4. Simplify square root expressions using the product rule and the quotient rule for radicals. 7.3
n
* product rule for radicals:
n
a
n
b
n
ab
* quotient rule for radicals:
n
a
b
n
a
b
5. Add or subtract square root expressions. You might need to simplify square roots or find common denominators
before they can be combined. Remember only like radicals may be combined (variables and their exponents have to
be the same both inside and outside the root to be like). 7.4
6. Multiply two square roots by using the distributive property or the FOIL method. If possible, simplify any square
roots that appear in the product. 7.4
7. Simplify a quotient involving square roots. Rationalize any denominators. 7.5
* For denominators with 1 term: get rid of the root in the bottom by multiplying top and bottom by what the denominator
needs to come out of the radical.
* For denominators with 2 terms: get rid of the root in the bottom by multiplying top and bottom by the denominator’s
conjugate (the same binomial but with opposite signs in the middle).
* For numerators and denominators with different indices, change to exponential form and combine exponents for factors of
the same base.
8. Solving radical equations by: 7.6
* For one radical: get the radical alone on one side of the equal sign, raise both sides to the power of the index, and solve
the remaining equation.
* For two radicals: get each radical to each side of the equal sign, raise both sides to the power of the index, and solve the
remaining equation.
* For two radicals and a non-radical: get one radical on one side and the other radical and non-radical to the other side of
the equal sign, raise both sides to the power of the index. You will still have a radical and need to repeat the process.
9. Solve problems involving radicals by using the Pythagorean Theorem. 7.6
10. Solve for specific variables in formulas involving radicals. 7.6
11. Perform operations involving complex numbers. This includes converting radicals to complex numbers,
adding, subtracting, multiplying, and dividing complex numbers. 7.7
12. Simplify powers of i 7.7
Practice Problems
The answer to all the problems listed below, even and odd, are in the back of the book. For those of you who have
the Chapter Test Prep Video cd that came with the book, you can use it to see someone solving each of the
problems in the Chapter Tests. If you don’t have it, it is available at the math lab.
Math 152B
Practice Exam 1: Chapter 7
Assume all variables represent non-negative real numbers.
1. Simplify.
5
32( x 2)
3. Simplify.
3
4
2. Simplify using absolute value.
n2 20n 100
5
4. Simplify.
6
(5 2ab4c6 )15
5. Simplify.
9
1
6 3
(125 x y )
6.
Multiply.
1
2
4 x (2 x
1
3
1
4
3x )
7.
Simplify.
8. Simplify.
50 x 3
81y 8
4
9. Simplify.
10. Add.
8 7
2m6n3
48a b
3a 2b
54xy 3
8m4n m2 18n
3
11. Add.
3
20 xy10
4 x13 y 2
12.
y3 128x
Multiply.
3
6 x7 y
3
9 x 4 y12
13. Multiply.
7 x ( 14 x
14. Multiply.
(3 5 2 3 )( 5
28 )
15. Multiply.
(3 m
3
6n )(3 m2
3
9n2 )
17. Rationalize the denominator.
6 9
4
405a b
4c3
5 3)
16. Rationalize the denominator.
7
3
2x2
18. Rationalize the denominator.
x
x
y
y
19. Simplify.
6
2 5
5
20. Simplify.
3
45
m4n2
4
m3n
21. Solve for x .
3
x 9 7
22. Solve for x .
5x 1 1
23. Solve for the unknown side.
24. Simplify.
3 5
70
x
10
a16b30
4x 3
25. Solve for d .
2d
V
c
26. Add or subtract.
27. Multiply.
28. Multiply.
(3
54 )(
4i(7 3i)
29. Divide.
2 5i
5 3i
( 5 7i) (8 12i) 4
30. Simplify.
i15
6
4)