Math 901: Algebra I Unit 1 Test Study Guide

Math 907 Test Study Guide
Algebra I Unit 7: Exponential and Radical Functions
1. Know and apply these properties of exponents:
m n m+ n
• Product of powers with same base: b ⋅b = b
m
b m−
n
• Quotient of powers with same base: = b
n
b
n
m mn
• Power of a power: b = b
( )
( ab)
m m m
• Power of a product: = a b
m
⎛ a ⎞ a
• Power of a quotient: ⎜ ⎟ =
m
⎝ b ⎠ b
− n 1 1
• Negative exponent:
b = and = b
n
− n
b b
0
• Zero exponent: b = 1
2. Evaluate algebraic expressions with given values.
3. Identify a given number as either rational or irrational.
4. Take a given number and write it in scientific notation.
5. Write radical expressions in simplest radical form.
6. Know and apply these properties of radicals:
n n n
• a ⋅ b = ab
n
a a
• n =
n
b b
m
n m
• b = b n
n n
• If n is even, x = x
m
n n
• If n is odd, x = x
n
• If x < 0, and n is even, then x is not real, b ut im aginary.
3 3 3 2
7. Rationalize radical denominators. e.g., = = ⋅ = 6
2 2 2 2 2
8. Simplify algebraic expressions by combining like radical terms.
9. Add, subtract, multiply and divide algebraic expressions involving radicals.
10. Solve equations that involve radicals.
11. Determine when there is no solution to an equation involving radicals. Be
sure to check solutions in the original equation. There is no real solution
for an even root of a negative number, e.g., 4 − 9 is not real. Also, an
n

even root can never equal a negative number, e.g., y − 1=−12has no real
solution.
12. Identify the common ratio of a geometric sequence.
13. Know and apply the explicit formula for geometric sequences:
n−1
A( n) = a1
⋅r
, where ...
th
A( n) = the actual value of the n term
st
a1
= the 1 term
r = the common ratio between consecutive terms
n = the counting number of the term, such as the 3rd term would have n = 3
14. Find a certain term of a given geometric sequence.