Beginning & Intermediate Algedra Review

0.10(10.5) Multiplying and Dividing Radical Expressions

Exercises 7-42
Multiply, then simplify the product. Assume that all variables represent positive real numbers.
 

Exercises 43-68
Rationalize the denominator. Assume that all variables represent positive real numbers.

Exercises 69-82
Simplify. Assume that all variables represent positive real numbers.

Exercises 85-100
Rationalize the denominator. Assume that all variables represent positive real numbers and that the
denominator is not zero.

Exercises 103-110
Write the expression in lowest terms. Assume that all variables represent positive real numbers.

0.11(4.1) The Product Rule and Power for Exponents

Exercises 5-12
Write the expression using exponents.

Exercises 15-22
Identify the base and the exponent for the exponential expression.
48) 3x¹²

A)Base:12,exponent:3x
B)Base:3x,exponent:12
C)Base:x,exponent:12
D)Base:12,exponent:x

Exercises 25-42
Simplify the expression. Use positive exponents. Assume variables represent nonzero real numbers.

Exercises 43-62
Use the power rules for exponents to simplify. Write the answer in exponential form.

Exercises 63-80
Simplify the expression. Use positive exponents. Assume variables represent nonzero real numbers.
  

Exercises 83-86
Solve the problem.
52) Find the area of the figure.
 

Exercises 91-94
Use the formula A = P(1+r)^n to find the amount of money in the bank account described. Use a
calculator, and round to the nearest cent.
53) P=$250, r=0.06,n=6

A) $454.63
B) $1590.00
C) $346,318,142,640,625.00
D) $354.63

0.12(4.2) Integer Exponents and the Quotient Rule

Exercises 1-10
Evaluate.

Exercises 17-28
Evaluate the expression.

Exercises 29-52
Simplify the expression. Use positive exponents. Assume variables represent nonzero real numbers.

Exercises 57-78
Use a combination of rules for exponents to simplify. Write answers with only positive exponents.
Assume that all variables represent nonzero real numbers.

0.13(10.2) Rational Expressions

Exercises 11-30
Simplify the expression involving rational exponents.

                                                                                                                                                                                                                                                                       Exercises 33-44
Write with radicals. Assume that all variables represent positive real numbers.
 

Exercises 47-56
Simplify by first converting to rational exponents. Assume that all variables represent positive real numbers.
 

Exercises 57-82
Use the rules of exponents to simplify the expression. Write the answer with positive exponents.
Assume that all variables represent positive real numbers.

Exercises 93-94
Solve the problem.
65) A formula for calculating the distance, d, one can see from an airplane to the horizon on a clear
day is d=1.22*1/2,where x is the altitude of th plane in feet and d is given in miles. How far
can one see in a plane flying at 27,000 feet? Round your answer to the nearest tenth mile, if necexsary.

A) 16,470 miles
B) 200.5 miles
C) 181.5 miles
D) 1647 miles

0.9(10.3) Simplifying Radical Expressions

Exercises 7-20
Multiply using the product rule.

Exercises 23-38
Simplify the radical. Assume that all variables represent positive real numbers.

Exercises 39-58
Express the radical in simplified form.