Name:_____________________________________________ Date: _____________________ Period:_____
Algebra 2
Review for Chapter 6 Test
Sections 6-1 to 6-5 and 6-7
*Rule: exponent inside radical must be smaller than the index
**Recall: You must use absolute value bars around an odd exponent answer of an even index!
Simplify.
1.
4
625 x 8 y 5
2.
3
0.008 x 2 y 6
3. 63 x 3 y 10 z 4
Recall: exponent of the radicand goes in the numerator of the rational exponent and the index goes in the
denominator of the rational exponent
Write each expression in exponential form.
4.
4
p6
5.
3
(a  b)15
Write each expression in radical form.
7. x  y 

6. 4 2.5
2
5
Properties of Radicals
n
a  n b  n ab
n
a n a

b
b
n
*Product Property: index must be the same
*Quotient Property: index must be the same
Take note: If the index is not the same, you must apply your exponent rules!
Review: Properties of Exponents:
b m  b n  b m n
(b m ) n  b mn
(ab) m  a m b m
m
am
a
   m
b
b
b
m
1
 m
b
bm
 b mn
n
b
b0  1
Simplify each expression. Assume all variables are positive.
5
64 x
8. 63  15x 2  3 9 x 5
9.
5
2 x 11 y 4
10. (441u 4 v 64 )
12. (9
1
2
1
 5 3 )3
1
2
11.
 
535
13. (2 3  33 )
1
3
Simplify each expression. Assume all variables are positive.
1
1
31
14. 1
15. 9 3  45 3
3 4
1
16. 27 
 1000a 9 c 8  3

17. 
3 4 
 343b c 
2
3
When Adding and Subtracting radicals: simplify each term and look to see if you can combine
like terms. Remember the radical stays the same when you add or subtract the coefficients of the radicals.
Simplify each expression.
18. 6 18  3 50

20. 3 2 5 8  2 2

22. 2 5  2

2
19. 33 81  23 54  3 2



21. 5  2 5 7  4 5
23.
5 3
2 3

Steps for Solving Radical Equations:
1. Isolate the radical or quantity raised to a fractional exponent on one side of the equation.
2. Get rid of the radical by raising each side to the power suggested by the index.
3. If the equation is in the form

, raise each side to the reciprocal power.
Use absolute value bars if either the numerator or the denominator of the fraction is even
4. Be sure to check your solution(s) for extraneous solutions!
Solve each equation. Check for extraneous solutions.
x  4 1
Check:
25. 2x  1 3  4  36
Check:
24.
3
4
26.
x  x 8  2
Check:
A Relation is in the form x, y  and its inverse is  y, x .
The graph of f
1
x 
is the graph of f x  reflected around the line _________________.
Find the inverse of each relation. Graph the given relation and its inverse.
27.
x
0
2
3
4
y
–1
0
2
3
28.
x
–2
–1
0
1
y
2
0
3
0
x
x
y
y
Find the inverse of each function. Is the inverse a function?
29. y  x  3  5
2
31. y 
1
x3
2
30. y  3
32. f x   5 x 2  2
The vertical line test will tell you if the relation is a function.
The horizontal line test will tell you if the inverse is a function.
Refer to the graphs below to answer the questions.
33.
Is this graph a function?
34.
_______________
Is this graph a function?
Is the inverse a function? _______________
35.
Is this graph a function?
_______________
Is the inverse a function? _______________
36.
_______________
Is the inverse a function? _______________
Is this graph a function?
_______________
Is the inverse a function? _______________
37. Which of the above problems are inverse functions? Question #__________