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EXPONENTS Zero and Negative
EXPONENTS
Zero and Negative
X2
X TO THE SECOND POWER
OR
X SQUAREDX IS CALLED BASE
2 IS CALLED EXPONENT
Use x as a factor 2 times
X * X
X3X TO THE THIRD POWER
OR
X CUBED
X IS CALLED BASE
3 IS CALLED EXPONENT
Use x as a factor 3 times
X * X *X
X4
X TO THE FOURTH POWER
X IS CALLED BASE
4 IS CALLED EXPONENT
Use x as a factor 4 times
X * X * X * X
323 TO THE SECOND POWER
OR
3 SQUARED
Use 3 as a factor 2 times
3 * 3
32 = 9
333 TO THE THIRD POWER
OR
3 CUBED
Use 3 as a factor 2 times
3 * 3 * 3
33 = 27
POWERS OF BASE 10
100 = 1101 = 10
102 = 100103 = 1000104 = 10,000105 = 100,000106 = 1,000,000
POWERS OF BASE 2
20 = 121 = 2
22 = 423 = 824 = 1625 = 3226 = 64
Any base to the zero power equals 1
Any base to the one power equals itself
2 x 22 x 2 x 22 x 2 x 2 x 22 x 2 x 2 x 2 x 22 x 2 x 2 x 2 x 2 x 2
POWERS OF BASE 3
30 = 131 = 3
32 = 933 = 2734 = 8135 = 24336 = 729
Any base to the zero power equals 1
Any base to the one power equals itself
3 x 33 x 3 x 33 x 3 x 3 x 33 x 3 x 3 x 3 x 33 x 3 x 3 x 3 x 3 x 3
TRY IT OUT
100 = 1
50 = 1
23 = 8
34 = 81
53 = 125
25 = 32
TRY IT OUT
103 =
160 = 1
62 = 36
52 = 25
43 = 64
73 = 343
1000
MULTIPLYING EXPONENTS
WITH THE SAME BASE
X2 * X3 = X5
X * X * X * X* X
Keep the base ADD the Exponents
(102) (103) = 105
10 * 10 * 10 * 10* 10
Keep the base ADD the Exponents
() () PARENTHESES mean TIMES
(Y3 X2) (Y4 X3) = Y7X5
(Y * Y * Y * X * X) * (Y * Y* Y * Y * X * X * X)
Keep the base ADD the Exponents
() () PARENTHESES mean TIMES
TRY IT OUT
5 * 5 2 * 5 3 = 5 6
Don’t forget the one exponent is implied
X * Y 2 * X 3 * Y = X 4 Y3
Don’t forget the one exponent is implied
TRY IT OUT
(XY3) ( X2 Y 3) = X3Y6
Don’t forget the one exponent is implied
(X2 Y2 Z 3) (Y4 Z5) = X 2 Y6 Z8
Don’t forget the one exponent is implied
DIVIDING EXPONENTS
WITH THE SAME BASE
X5 / X3 = X2
Keep the base SUBTRACT the Exponents
106 / 102 = 104
Keep the base SUBTRACT the Exponents
Negative Exponents
• Negative exponents are NOT negative numbers
• Negative exponents are fractions or decimals
• Negative exponents are greater than 0 but less than one
Examples
10-3 = 1
103
OR 1
1000
OR 0.001
Examples
2-3 = 1
23
OR 1
8
OR 0.125
Examples
2-3 = 1
23
OR 1
8
OR 0.125
Negative ExponentTo ReciprocalTo FractionTo Decimal
MORE EXAMPLES
10 –1 = 1 = 1 = 0.1
101 10
10 –2 = 1 = 1 = 0.01
102 100
MORE EXAMPLES
10 –3 = 1 = 1 = 0.001
103 1000
10 –4 = 1 = 1 = 0.0001
104 10000
MORE EXAMPLES
10 –5 = 1 = 1 = 0.00001
105 100,000
10 –6 = 1 = 1 = 0.000001
106 1,000,000
Created by:pmastro.weebly.com/uploads/2/8/2/7/.../exponents.801116.ppt
