EXPONENTS

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EXPONENTS
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Recall Pascals Triangle
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Recall Pascals Triangle
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Recall Pascals Triangle
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Recall Pascals Triangle
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Recall Pascals Triangle
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Recall Pascals Triangle
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Recall Pascals Triangle
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Recall Pascals Triangle
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Recall Pascals Triangle
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Recall Pascals Triangle
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Recall Pascals Triangle
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Recall Pascals Triangle
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Recall Pascals Triangle
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Recall Pascals Triangle
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Recall Pascals Triangle
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Recall Pascals Triangle
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Recall Pascals Triangle
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Recall Pascals Triangle
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Recall Pascals Triangle
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Recall Pascals Triangle
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Recall Pascals Triangle
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Recall Pascals Triangle
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1

This pattern continues forever.
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Pascals Triangle is filled with patterns.
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1

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Increasing by one.
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1

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Increasing by 2, then 3, then 4, then 5.
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10
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15
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1

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Increasing by 3, then 6, then 10, then 15.
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1
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4
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1
5
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10
10
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1
6
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15
15
20
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1

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Pascals Triangle also has symmetry.
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10
10
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15
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1

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Some patterns are not very obvious.
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6
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5
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10
10
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1
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15
20
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1
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Some patterns are not very obvious.
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3
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1
4
4
6
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5
5
10
10
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1
6
6
15
15
20
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1
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Calculate the sum of each row.
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1
2
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1
3
3
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1
4
4
6
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1
5
5
10
10
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1
6
6
15
15
20
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1
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Calculate the sum of each row.
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1
ROW 1
1
1
2
1
1
3
3
1
1
4
4
6
1
1
5
5
10
10
1
1
6
6
15
15
20
1
1
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Calculate the sum of each row.
1
1
ROW 1
1
1
ROW 2

2
2
1
1
3
3
1
1
4
4
6
1
1
5
5
10
10
1
1
6
6
15
15
20
1
1
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Calculate the sum of each row.
1
1
ROW 1
1
1
ROW 2

2
2
1
1
ROW 3
4


3
3
1
1
4
4
6
1
1
5
5
10
10
1
1
6
6
15
15
20
1
1
36
Calculate the sum of each row.
1
ROW 1
1
1
1
ROW 2

2
2
1
1
ROW 3
4


8
3
3
1
1
ROW 4



4
4
6
1
1
5
5
10
10
1
1
6
6
15
15
20
1
1
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Calculate the sum of each row.
1
ROW 1
1
1
1
ROW 2

2
2
1
1
ROW 3
4


8
3
3
1
1
ROW 4



4
4
6
1
1
ROW 5
16




5
5
10
10
1
1
6
6
15
15
20
1
1
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Lets chart our findings.
1
ROW 1
1
1
1
ROW 2

2
2
1
1
ROW 3
4


8
3
3
1
1
ROW 4



4
4
6
1
1
ROW 5
16




5
5
10
10
1
1
ROW 6
32





6
6
15
15
20
1
1
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Lets chart our findings.
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The sum of a particular row is double the sum of
the previous row.
X 2
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Each sum can be written as the product of twos.
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Each sum can be written as the product of twos.
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Expressions that multiply the same number over
and over again can be written using exponents.
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Expressions that multiply the same number over
and over again can be written using exponents.
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Expressions that multiply the same number over
and over again can be written using exponents.
46
Expressions that multiply the same number over
and over again can be written using exponents.
47
Expressions that multiply the same number over
and over again can be written using exponents.
48
Expressions that multiply the same number over
and over again can be written using exponents.
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What is the exponential expression that equals 1 ?
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What is the exponential expression that equals 1 ?
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What is the exponential expression that equals 1 ?
Any base raised to the power of zero is always 1.
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Every exponential expression has a base and an
exponent.
3 is the exponent.
5
3
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Every exponential expression has a base and an
exponent.
5
3
5 is the base.
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Every exponential expression has a base and an
exponent.
5
3
The base tells you what number to write down.
5
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Every exponential expression has a base and an
exponent.
The exponent of 3 means to write the number 3
times.
5
3
5
5
5
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Every exponential expression has a base and an
exponent.
5
3
Exponents always imply multiplication.
5
5
5
X X
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Every exponential expression has a base and an
exponent.
5
3
Exponents always imply multiplication.
5
5
5 125
X X
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Practice Time
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1) What is the missing entry?
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2) What is the missing entry?
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3) What is the missing entry?
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4) What is the missing entry?
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5) What is the missing entry?
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6) Complete the table.
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7) Complete the table.
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8) Complete the table.
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9) Complete the table.
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10) Complete the table.
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11) Complete the table.
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12) Complete the table.
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13) Evaluate the following expression if x6 and
y3.
xy
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13) Evaluate the following expression if x6 and
y3.
63
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13) Evaluate the following expression if x6 and
y3.
63 6 x 6 x 6
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13) Evaluate the following expression if x6 and
y3.
63 6 x 6 x 6
216
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14) Evaluate the following expression if x2,
y3, and z4
zxy
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14) Evaluate the following expression if x2,
y3, and z4
423
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14) Evaluate the following expression if x2,
y3, and z4
423 4 2 2 2
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14) Evaluate the following expression if x2,
y3, and z4
423 4 2 2 2 32
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THE END!