7.5 Properties of Exponents and Scientific Notation

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7.5 Properties of Exponents and Scientific
Notation
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Exponents and Exponential Expressions

• Exponents are used to write products of repeated
  factors.
• Ex. 3 3 3 3 34
• In the above example, the 4 is the exponent and 3
  is the base.
• The quantity 34 is called an exponential
  expression.

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Evaluating Exponential Expressions

• Evaluate each exponential expression.
• 72
• -42
• (-2)4

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? Evaluate each exponential expressions.

• 51
• 53
• -84
• (-2)5
• -24

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The Product Rule

• Product Rule for Exponents
• am an am n
• Apply the product rule for exponents in each
  case.
• 34 37
• (5y2)(-3y4)

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?Apply the product rule for exponents in each
case.

• 53 5
• y3 y8 y2
• (7p3q)(2p5q2)

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The Power Rules

• Power Rules for Exponents

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Applying the Power Rules

• Simplify each expression.
• (p8)3 (3y)4

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? Simplify each expression.

• (6p7)2

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Zero and Negative Exponents

• Zero Exponent
• a0 1
• Negative Exponent
• Special Rules for Negative Exponents

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Evaluating Exponential Expressions

• Evaluate each expression.
• 120 5z-3 -60
• (-m)-4 (8k)0 2-3
• 3-1 4-1

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The Quotient Rule

• Quotient Rule for Exponents

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Applying the Quotient Rule

• Simplify each quotient.

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Writing Expressions with No Negative Exponents

• Simplify each expression so that no negative
  exponents appear in the final result.
• 32 3-5 (x-4)6

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?Simplify each expression so that no negative
exponents appear in the final result.

• x-3 x-4 x2 (4-2)-5 (23x-2)-2

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Scientific Notation

• Many of the numbers that occur in science are
  very large or very small.
• Writing these numbers is simplified by using
  scientific notation.
• Scientific Notation
• A number is written in scientific notation when
  it is expressed in the form a x 10n, where 1
  alt 10 and n is an integer.

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IB Exam Information(NOT in your book!)

• Express your answer in the form a x 10k, where 1
  alt 10 and k ? .
• FYI
• ? means is an element of
• represents all integers

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Converting to Scientific Notation

• Convert each number from standard notation to
  scientific notation.
• 8,200,000
• .000072

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?Convert each number from standard notation to
scientific notation.

• 46,500
• .0051

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Converting from Scientific Notation

• Convert each number from scientific notation to
  standard notation.
• 6.93 x 105
• 4.7 x 10-6

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?Convert each number from scientific notation to
standard notation.

• 2.317 x 105
• 1.63 x 10-4

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Using Scientific Notation in Computation

• Evaluate by
  using scientific
• notation.

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?Evaluate the following by using scientific
notation.