Algebra 1A Vocabulary 1-2ReviewProblem 5

Suppose you draw a segment from any one vertex of a regular polygon to the other vertices. A sample for a regular hexagon is shown above. Use the table to find a pattern. What is a rule for the number of nonoverlapping triangles formed?

Problem 5Number of Sides of Polygon Number of Triangles

Give a rule in words to find the number of nonoverlapping triangles in a polygon.

Write an algebraic expression for the number of nonoverlapping triangles in a polygon that has n sides.

ReviewWhat is a variable?What does a numerical expression contain?What does an algebraic expression contain?Give an example of an operation.

An exponent is a shorthand notation for repeated multiplication.

3 • 3 • 3 • 3 • 3

3 is a factor 5 times

Using an exponent, this product can be written as

35exponent

base

Exponents

This is called exponential notation. The exponent, 5, indicates how many times the base, 3, is a factor.

35exponent

base

Read as “three to the fifth power” or “the fifth power of three.”

3 • 3 • 3 • 3 • 3

3 is a factor 5 times

Exponential Notation

SimplifyYou simplify a numerical expression when you

replace it with its single numerical value.Example:

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4⋅ 9 is 36,

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34 = 3⋅ 3⋅ 3⋅ 3 = 81

To simplify a power, you replace it with its simplest name,

For example,

The simplest being 81.

Sample Problems1. What is the simplest form of each expression?

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A. 107

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B. 25 ⎛ ⎝ ⎜

⎞ ⎠ ⎟2

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C. 0.4( )3

Order of OperationsWhen simplifying algebraic expressions with

more than one operation, you have to make a decision about what order to perform the operations.

For example,

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2 + 3⋅ 5

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Could be 2 + 3( )⋅ 5

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or 2 + 3⋅ 5( )

1. Perform all operations within parentheses ( ), brackets [ ], or other grouping symbols such as fraction bars, starting with the innermost set.

2. Simplify powers.3. Multiply or divide in order from left

to right.4. Add or subtract in order from left to

right.

Rules for Order of Operations

Sample Problems1. What is the simplified form of each expression?

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A. 6 - 2( )2 ÷ 2

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B. 24 −1

5

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C. 75 ÷ 33 − 2( )