Chapter 1'3 Exponents and Powers

1
Chapter 1.3 Exponents and Powers

• Goals
• How to evaluate expressions containing exponents
• How to use exponents in real-life problems
• Why?
• You can use exponents to simplify writing in
  algebra as in the formula for the area of a
  square, A s².

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Expressions Containing Exponents

• 4³ 4 4 4
• There are 3 factors of 4
• The number 4 is the base, the number 6 is the
  exponent, and the number 4³ is a power.
• 7² is read as seven to the second power or seven
  squared
• 4³ is read as four to the third power or four
  cubed
• 5¹ 5, the one is impliedit is the
  multiplicative identity

3
Power, Base, Exponent

• Multiply a number, even a small one like three,
  by itself over and over and the product gets very
  large very fast. A few bacteria can grow into a
  colony of billions in a matter of hours by
  doubling every 20 minutes. Mathematicians use
  shortcuts like powers, roots, and logarithms to
  describe such situations.
• A POWER is a number w/ a base and an exponent,
  such as 6³. When you use an exponent, the BASE
  is a repeated factor. The exponent tells how
  many times the base is used as a factor.
• 6 6 6 6³ 216
• When you understand powers, you also understand
  roots. A ROOT is the inverse (opposite) of a
  power. The square root is one of a numbers two
  equal factors. The cube root is one of a
  numbers tree equal factors. ³ 216 6

4
Question?

• How many different factors are in this
  expression?
• 4 4 4 4 7 7
• 2
• How many factors of 3 are there in this
  expression?
• 2 2 2 3 3 3 3 3 5
• 5

5
Evaluating an Algebraic Expression Involving an
Exponent

• Evaluate the expression (3a 6b)² when a 1 and
  b 2.
• 3(1) 6(2) ²
• Evaluate 2x³ and (2x)³ when x 4.

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Using Exponents

• Many formulas for area and volume involve
  exponents. In fact, the words squared and cubed
  come from the formulas for the area of a square,
  A s², and the volume of a cube, V s³.
• Use exponents to write a formula for the surface
  are of a cube. Then use the formula to find the
  surface area of a cube whose edges are each 3
  inches.
• Epcot center has a diameter of 165 ft and is
  shaped like a sphere. What is the approximate
  surface area given the formula, S 4?r²

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Assignment

• 1-34 Even