Integer Exponents and Scientific Notation Section 0.2

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Integer Exponents and Scientific NotationSection
0.2
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Whats an exponent?

• Exponents are shorthand notation for repeated
  multiplication
• 5?5?5?5 54
• There are four 5s being multiplied together.
• In 54 , the 5 is called the base and the 4 is the
  power or exponent.
• In 5?5?5?5 , the 5s are called factors.

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Evaluating expressions

• Evaluating an expression means to find out what
  its worth (giving its value)just do the math.

(note that the location of the negative sign and
the parenthesis make a difference in the answer!)
Evaluate the following
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Evaluating expressions continued
Evaluate the following 32?34
This can become 3?3?3?3?3?3
or 36
Which is 729
This idea is called the Product Property of
Exponents. When you are multiplying exponentials
with the same base you add the exponents. Just
remember the bases MUST be the same.
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More properties of exponents
This can become
Remember that a number divide by itself is 1
So all that is left is 5?5 which is 25. This is
the Quotient Properties of Exponents. When you
divide exponentials with the same base, subtract
the exponents.
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More properties of exponents
Power property of exponents
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More properties of exponents
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EXAMPLES
Evaluate numeric expressions
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Simplifying Algebraic Expressions

• Algebraic expressions are simplified when the
  following things have happened or are done
• All parenthesis or grouping symbols have been
  eliminated
• A base only appears once
• No powers are raised to other powers
• All exponents are positive

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EXAMPLES
Simplify algebraic expressions
Product of powers property
a. b4b6b7
Power of a quotient property
Power of a power property
r6s9
Negative exponent property
Quotient of powers property
8m4n 5 (5)
8m4n0 8m4
Zero exponent property
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EXAMPLE
Standardized Test Practice
SOLUTION
The correct answer is B
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More Examples
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More Examples
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GUIDED PRACTICE
Simplify the expression. Tell which properties
of exponents you used.
x6x5 x3
x2 Product of powers property
ANSWER
(7y2z5)(y4z1)
Product of powers property, Negative exponent
property
ANSWER
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GUIDED PRACTICE
Power of a power property, Negative exponent
property
ANSWER
Quotient of powers property, Power of a
Quotient property, Negative exponent property
ANSWER
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Scientific Notation
Scientific Notation was developed in order to
easily represent numbers that are either very
large or very small. Following are two examples
of large and small numbers. They are expressed in
decimal form instead of scientific notation to
help illustrate the problem
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 A very large number                             
                 The Andromeda Galaxy (the
closest one to our Milky Way galaxy) contains at
least 200,000,000,000 stars.
                   
A very small number On the other hand, the
weight of an alpha particle, which is emitted in
the radioactive decay of Plutonium-239,
is0.000,000,000,000,000,000,000,000,006,645
kilograms. As you can see, it could get tedious
writing out those numbers repeatedly. So, a
system was developed to help represent these
numbers in a way that was easy to read and
understand Scientific Notation.
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Decimal to Scientific Notation

• Move the decimal point so the number shown is
  between 1 and 10
• Count the number of spaces moved and this is the
  exponent on the 10
• If the original number is bigger than 1, the
  exponent is positive
• If the original number is between 0 and 1, then
  the exponent is negative.

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What to do for scientific notation
Write in scientific notation 200,000,000,000
So we write the number in scientific notation as
2.0 x 1011
Write in scientific notation 0.000,000,000,000,0
00,000,000,000,006,645
6.645 x 10-27
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Scientific Notation to Decimal

• The number of spaces moved is the exponent on the
  10
• Move to the right if the exponent is positive
• Move to the left if the exponent is negative

6.45 x 104
64,500
2.389 x 10-6
.000002389