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Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
1
August 22, 2017
Aug 223:22 PM
WARM UP
Simplify using order of operations.
SOLUTION
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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Aug 224:09 PM
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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a) The equation 3(4x) = (4x)3 illustrates which property?
WARM UP
b) Which property of real numbers is illustrated by the equation :
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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c) If M, P and Q represent integers, M = P and
P = Q then M = Q is an example of which
property?
d) The equation 5 + (3x + 4) = (5 + 3x) + 4 illustrates which property?
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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Aug 193:11 PM
Homework Assignment
The following examples have to be copied for next class
Example 3
The examples must be copied and ready for me to check once you come to class.
Example 5
Example 6
Example 7
Example 8
Example 10
Example 11
Example 14
Example 15
Example 17
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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Aug 196:29 AM
Rules of Exponents
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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The Zero Exponent Rule
If b is any real number other than 0, then
also zero raised to the zeroth power is undefined.
is undefined
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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SOLUTION
EXAMPLE 1
Simplify :
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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Aug 1512:15 PM
SOLUTION
EXAMPLE 2
Simplify :
1
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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Jul 176:25 PM
SOLUTION
EXAMPLE 3
Simplify :
1
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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SOLUTION
EXAMPLE 4
Simplify :
1
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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SOLUTION
EXAMPLE 5
Simplify :
1
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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Opposite of a Power
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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SOLUTION
EXAMPLE 6
Simplify :
Raise 2 to the 3rd power then take the opposite of this number.
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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SOLUTION
EXAMPLE 7
Simplify :
Raise 6 to the 0th power then take the opposite of this number.
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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August 22, 2017
Jul 1810:28 AM
Changing the sign of an Exponent
If a term in the numerator is moved to the
denominator the exponent will now have the
opposite sign. (If the exponent was negative
it will become positive and vice versa.)
The same is true if a term in the denominator
is moved to the numerator the exponent will
now have the opposite sign.
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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Jul 1810:33 AM
SOLUTION
EXAMPLE 8For the following expression if a term was originallyin the numerator move the term to the denominator.If a term was originally in the denominator move theterm to the numerator.
Rewrite the expression so that every term has an exponent.
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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Jul 1810:43 AM
Move only the terms in the numerator to the denominator. Keep in mind the only thing that should change is the exponent will now have the opposite sign.
Now move the terms that were originally in the denominator to the numerator. Keep in mind the only thing that shouldchange is the exponent will now have the opposite sign.
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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Aug 152:01 PM
SOLUTION
EXAMPLE 9Rewrite the expression with only positive exponents :
Rewrite the expression so that every term has an exponent.
Move any term to the denominator that has a negative exponent
in the numerator.
we only move a term if the exponent is negative, Notice that the –5 did not move to the denominator,
not the number itself.
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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Move any term to the numerator that has a negative exponent in the denominator.
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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SOLUTION
EXAMPLE 10Rewrite the expression with only positive exponents :
Rewrite the expression so that every term has an exponent.
Move any term to the denominator that has a negative exponent
in the numerator.
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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Jul 177:23 PM
SOLUTION
EXAMPLE 11Rewrite the expression with only positive exponents :
Move any term to the denominator that has a negative exponent in the numerator.
Whenever the numerator does not have a value place a 1 in the numerator.
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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Jul 1811:01 AM
SOLUTION
EXAMPLE 12
Move any term to the denominator that has a negative exponent in the numerator.
Rewrite the expression with only positive exponents :
Whenever the numerator does not have a value place a 1 in the numerator.
Notice that only the exponent has an opposite sign, the –2 has the same sign.
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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August 22, 2017
Aug 196:58 AM
Product Rule with
When multiplying exponential expressions with
the same nonzero base, ADD the exponents. Use
this sum as the exponent of the common base.
the same base
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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SOLUTION
Since we are multiplying powers with the same bases use the product to simplify the expression.
EXAMPLE 13
Simplify :
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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SOLUTION
EXAMPLE 14
Simplify :
Rewrite the expression so that every term has an exponent.
Rearrange so that like terms are grouped together.
Because we are multiplying powers with the same base apply the product rule.
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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August 22, 2017
Jul 175:37 PM
SOLUTION
EXAMPLE 15
Simplify :
Rewrite the expression so that every term has an exponent.
Rearrange so that like terms are grouped together.
Because we are multiplying powers with the same base apply the product rule.
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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August 22, 2017
Aug 197:17 AM
Quotient Rule with
When dividing exponential expressions with
the same nonzero base, SUBTRACT the
exponent in the numerator minus the exponent
in the denominator. Use the difference as the
exponent of the common base.
the same base
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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Since the bases are the same we can keep thecommon base and subtract the exponents.
SOLUTION
EXAMPLE 16
Simplify :
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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Jul 1811:57 AM
SOLUTION
EXAMPLE 17
Simplify the expression the final answer should only have positive exponents.
Apply the quotient rule the fraction bar implies dividing.
Rearrange so that like terms are grouped together.
Rewrite the expression so that every term has an exponent.
Rules of Exponents Part 1[Algebra 1](InClass Version).notebook
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Jul 1811:34 AM
Rewrite the expression so that all the exponents are positive.
Keep in mind that only negative exponents are going to be moved negative numbers remain in place.