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7.5 Properties of Exponents and Scientific Notation

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7.5 Properties of Exponents and Scientific Notation Exponents and Exponential Expressions Exponents are used to write products of repeated factors. – PowerPoint PPT presentation

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Title: 7.5 Properties of Exponents and Scientific Notation


1
7.5 Properties of Exponents and Scientific
Notation
2
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.

3
Evaluating Exponential Expressions
  • Evaluate each exponential expression.
  • 72
  • -42
  • (-2)4

4
? Evaluate each exponential expressions.
  • 51
  • 53
  • -84
  • (-2)5
  • -24

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

6
?Apply the product rule for exponents in each
case.
  • 53 5
  • y3 y8 y2
  • (7p3q)(2p5q2)

7
The Power Rules
  • Power Rules for Exponents

8
Applying the Power Rules
  • Simplify each expression.
  • (p8)3 (3y)4

9
? Simplify each expression.
  • (6p7)2

10
Zero and Negative Exponents
  • Zero Exponent
  • a0 1
  • Negative Exponent
  • Special Rules for Negative Exponents

11
Evaluating Exponential Expressions
  • Evaluate each expression.
  • 120 5z-3 -60
  • (-m)-4 (8k)0 2-3
  • 3-1 4-1

12
The Quotient Rule
  • Quotient Rule for Exponents

13
Applying the Quotient Rule
  • Simplify each quotient.

14
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

15
?Simplify each expression so that no negative
exponents appear in the final result.
  • x-3 x-4 x2 (4-2)-5 (23x-2)-2

16
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.

17
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

18
Converting to Scientific Notation
  • Convert each number from standard notation to
    scientific notation.
  • 8,200,000
  • .000072

19
?Convert each number from standard notation to
scientific notation.
  • 46,500
  • .0051

20
Converting from Scientific Notation
  • Convert each number from scientific notation to
    standard notation.
  • 6.93 x 105
  • 4.7 x 10-6

21
?Convert each number from scientific notation to
standard notation.
  • 2.317 x 105
  • 1.63 x 10-4

22
Using Scientific Notation in Computation
  • Evaluate by
    using scientific
  • notation.

23
?Evaluate the following by using scientific
notation.
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