# 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

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.

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