This chapter is
divided into three parts:
I. Simplifying Rules
II. Complex Expressions with Exponents
III. Manipulating Complex Expressions
I. Simplifying
Rules
A. Exponent Rules
B. Simplifying Expressions
A. Exponent Rules
This
section is intended as a basic review of algebra; skim the material
and review what is necessary. When attempting to solve algebra
problems, it is important that you strictly follow the laws concerning
exponents.
Rule I: Add the exponents when multiplying two powers
of the same base:
3
3
= 3
Rule II: Multiply the exponents when obtaining the
power of a power:
(3)= 3
Rule III: Subtract the exponents when dividing a
power of a specified base by another power of the same base:
3/3
= 3
a negative exponent is
the equivalent of (1/the number) raised to the power. For
example, 3
= 1 / 3or
1 / 9.
Rule IV: The power of a product of factors
is written by raising each factor to the specified power. In
general,
(abc) = abc
Rule V: The power of a fraction is written by raising
the numerator and the denominator to the specified power. This
is expressed by
(a/b) = a/b
B. Simplifying
Expressions
Rule I: Perform multiplications and divisions before
you perform additions and subtractions. The expression x + 2y/3
is not the same as (x+2y)/3.
Rule II: Combine all like terms in an expression. The
expression 2x + x - y+
4y is simplified by combining the like
terms resulting in 3x + 3y.
Rule III: Perform operations inside parentheses first.
The expression (x + 2y)/3 is not the same as x + 2y/3.
With the parentheses present, we add first, then divide; with
no parentheses, we use Rule I and divide first, then add.
Rule IV: Eliminate inner parentheses first and the outermost
parentheses last. In the expression x(x + 2(3x + 4) -3), we remove
the inner parentheses first obtaining x(x + 6x + 8 - 3); then
we combine like terms giving x(7x + 5). We may then remove the
last parentheses providing 7x
+ 5x. Often brackets and braces are used if two or three sets
of parentheses are needed.
w II. Complex Expressions with Exponents
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