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Introducing Powers © T Madas
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A power is a shorthand for writing a number multiplied by itself
2 5 x 5 2 times = 5 5 to the power of 2 5 squared 5 multiplied by itself © T Madas
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A power is a shorthand for writing a number multiplied by itself
THIS IS NOT 5 x 2 2 5 x 5 = 5 © T Madas
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A power is a shorthand for writing a number multiplied by itself
2 8 x 8 2 times = 8 8 to the power of 2 8 squared 8 multiplied by itself © T Madas
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A power is a shorthand for writing a number multiplied by itself
2 6 x 6 2 times = 6 6 to the power of 2 6 squared 6 multiplied by itself © T Madas
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A power is a shorthand for writing a number multiplied by itself
3 5 x 5 x 5 3 times = 5 5 to the power of 3 5 cubed 5 multiplied by itself © T Madas
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A power is a shorthand for writing a number multiplied by itself
3 9 x 9 x 9 3 times = 9 9 to the power of 3 9 cubed 9 multiplied by itself © T Madas
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A power is a shorthand for writing a number multiplied by itself
7 x 7 x 7 x 7 = 74 7 to the power of 4 2 x 2 x 2 x 2 x 2 = 25 2 to the power of 5 11 to the power of 2 11 squared 11 x 11 = 112 1.2 x 1.2 x 1.2 = 1.23 1.2 to the power of 3 1.2 cubed © T Madas
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The Square Numbers 1, 4, 9, 16, 25, 36, … 12 22 32 42 52 62 … © T Madas
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© T Madas
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23 + 42 = 43 – 62 = 53 + 24 – 102 = 8 + 16 = 64 – 36 = 125 + 16 – 100 = 24 28 41 3 x 42 = 6 x 52 = 23 x 32 = 3 x 16 = 6 x 25 = 8 x 9 = 48 150 72 42 x 52 = 24 + 3 x 52 = 16 x 25 = 16 + 3 x 25 = 400 16 + 75 = 91 © T Madas
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Carry out the following substitutions:
x = 3 2x 2 = 2 x 32 = 2 x 9 = 18 x = 2 4x 3 = 4 x 23 = 4 x 8 = 32 x = 3 (2x )2 = ( 2 x 3 ) 2 = 6 2 = 36 x = 5 2x 2 + 3x = 2 x 52 + 3 x 5 = 2 x 25 + 15 = 65 © T Madas
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© T Madas
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Calculate the following powers:
32 = 3 x 3 = 9 62 = 6 x 6 = 36 52 = 5 x 5 = 25 53 = 5 x 5 x 5 = 125 23 = 2 x 2 x 2 = 8 43 = 4 x 4 x 4 = 64 33 = 3 x 3 x 3 = 27 13 = 1 x 1 x 1 = 1 42 = 4 x 4 = 16 112 = 11 x 11 = 121 82 = 8 x 8 = 64 24 = 2 x 2 x 2 x 2 = 16 © T Madas
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Calculate the following powers:
102 = 10 x 10 = 100 1002 = 100 x 100 = 10000 92 = 9 x 9 = 81 132 = 13 x 13 = 169 23 = 2 x 2 x 2 = 8 202 = 20 x 20 = 400 33 = 3 x 3 x 3 = 27 103 = 10 x 10 x 10 = 1000 72 = 7 x 7 = 49 152 = 15 x 15 = 225 122 = 12 x 12 = 144 34 = 3 x 3 x 3 x 3 = 81 © T Madas
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Calculate the following powers:
0.22 = 0.2 x 0.2 = 0.04 0.52 = 0.5 x 0.5 = 0.25 1.22 = 1.2 x 1.2 = 1.44 1.52 = 1.5 x 1.5 = 2.25 0.72 = 0.7 x 0.7 = 0.49 0.53 = 0.5 x 0.5 x 0.5 = 0.125 0.43 = 0.4 x 0.4 x 0.4 = 0.064 © T Madas
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© T Madas
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Calculate the following powers:
32 = 3 x 3 = 9 62 = 6 x 6 = 36 52 = 5 x 5 = 25 53 = 5 x 5 x 5 = 125 23 = 2 x 2 x 2 = 8 43 = 4 x 4 x 4 = 64 33 = 3 x 3 x 3 = 27 13 = 1 x 1 x 1 = 1 42 = 4 x 4 = 16 112 = 11 x 11 = 121 82 = 8 x 8 = 64 24 = 2 x 2 x 2 x 2 = 16 © T Madas
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Calculate the following powers:
102 = 10 x 10 = 100 1002 = 100 x 100 = 10000 92 = 9 x 9 = 81 132 = 13 x 13 = 169 23 = 2 x 2 x 2 = 8 202 = 20 x 20 = 400 33 = 3 x 3 x 3 = 27 103 = 10 x 10 x 10 = 1000 72 = 7 x 7 = 49 152 = 15 x 15 = 225 122 = 12 x 12 = 144 34 = 3 x 3 x 3 x 3 = 81 © T Madas
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Calculate the following powers:
0.22 = 0.2 x 0.2 = 0.04 0.52 = 0.5 x 0.5 = 0.25 1.22 = 1.2 x 1.2 = 1.44 1.52 = 1.5 x 1.5 = 2.25 0.72 = 0.7 x 0.7 = 0.49 0.53 = 0.5 x 0.5 x 0.5 = 0.125 0.43 = 0.4 x 0.4 x 0.4 = 0.064 © T Madas
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© T Madas
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Evaluate the following:
= 9 + 8 = 17 = 125 + 4 = 129 42 – 23 = 16 – 8 = 8 82 – 72 = 64 – 49 = 15 = 9 + 16 = 25 = 64 + 8 = 72 52 – 22 = 25 – 4 = 21 62 – 32 = 36 – 9 = 27 = 9 + 9 = 18 = 32 + 8 = 40 33 – 23 = 27 – 8 = 19 53 – 52 = 125 – 25 = 100 = 16 + 8 = 24 = 81 + 8 = 89 © T Madas
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Evaluate the following:
= 16 + 8 = 24 = 125 + 9 = 134 52 – 23 = 25 – 8 = 17 92 – 72 = 81 – 49 = 32 = 36 + 16 = 52 = 64 + 27 = 91 72 – 32 = 49 – 9 = 40 102 – 32 = 100 – 9 = 91 = 16 + 16 = 32 = 64 + 8 = 72 33 – 24 = 27 – 16 = 11 43 – 42 = 64 – 16 = 48 = 32 + 16 = 48 = 81 + 64 = 145 © T Madas
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© T Madas
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Evaluate the following:
= 9 + 8 = 17 = 125 + 4 = 129 42 – 23 = 16 – 8 = 8 82 – 72 = 64 – 49 = 15 = 9 + 16 = 25 = 64 + 8 = 72 52 – 22 = 25 – 4 = 21 62 – 32 = 36 – 9 = 27 = 9 + 9 = 18 = 32 + 8 = 40 33 – 23 = 27 – 8 = 19 53 – 52 = 125 – 25 = 100 = 16 + 8 = 24 = 81 + 8 = 89 © T Madas
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Evaluate the following:
= 16 + 8 = 24 = 125 + 9 = 134 52 – 23 = 25 – 8 = 17 92 – 72 = 81 – 49 = 32 = 36 + 16 = 52 = 64 + 27 = 91 72 – 32 = 49 – 9 = 40 102 – 32 = 100 – 9 = 91 = 16 + 16 = 32 = 64 + 8 = 72 33 – 24 = 27 – 16 = 11 43 – 42 = 64 – 16 = 48 = 32 + 16 = 48 = 81 + 64 = 145 © T Madas
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x2 x-1 x3 π . EXP Ans = 1 2 3 + – 4 5 6 x ÷ 7 8 9 DEL AC ^ x! d/c RCL
. EXP Ans = 1 2 3 + – 4 5 6 x ÷ 7 8 9 DEL AC RCL ENG ( ) , M+ (–) . , ,, hyp sin cos tan a b/c x2 log ln x-1 nCr Pol( REPLAY ^ SHIFT ALPHA MODE ON x! nPr Rec( x3 d/c 10x ex sin-1 cos-1 tan-1 M- OFF STO π DRG› % Rnd Ran# A B C D E F X Y M ; e : CLR © T Madas
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. EXP Ans = 1 2 3 + – 4 5 6 x ÷ 7 8 9 DEL AC RCL ENG ( ) , M+ (–) . , ,, hyp sin cos tan a b/c x2 log ln x-1 nCr Pol( REPLAY ^ SHIFT ALPHA MODE ON x! nPr Rec( x3 d/c 10x ex sin-1 cos-1 tan-1 M- OFF STO π DRG› % Rnd Ran# A B C D E F X Y M ; e : CLR 3 1 2 961 3 1 x2 = 312 = 961 © T Madas
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. EXP Ans = 1 2 3 + – 4 5 6 x ÷ 7 8 9 DEL AC RCL ENG ( ) , M+ (–) . , ,, hyp sin cos tan a b/c x2 log ln x-1 nCr Pol( REPLAY ^ SHIFT ALPHA MODE ON x! nPr Rec( x3 d/c 10x ex sin-1 cos-1 tan-1 M- OFF STO π DRG› % Rnd Ran# A B C D E F X Y M ; e : CLR 6 5 2 4225 6 5 x2 = 652 = 4225 © T Madas
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. EXP Ans = 1 2 3 + – 4 5 6 x ÷ 7 8 9 DEL AC RCL ENG ( ) , M+ (–) . , ,, hyp sin cos tan a b/c x2 log ln x-1 nCr Pol( REPLAY ^ SHIFT ALPHA MODE ON x! nPr Rec( x3 d/c 10x ex sin-1 cos-1 tan-1 M- OFF STO π DRG› % Rnd Ran# A B C D E F X Y M ; e : CLR . 7 6 2 0.5776 . 7 6 x2 = 0.762 = 0.5776 © T Madas
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. EXP Ans = 1 2 3 + – 4 5 6 x ÷ 7 8 9 DEL AC RCL ENG ( ) , M+ (–) . , ,, hyp sin cos tan a b/c x2 log ln x-1 nCr Pol( REPLAY ^ SHIFT ALPHA MODE ON x! nPr Rec( x3 d/c 10x ex sin-1 cos-1 tan-1 M- OFF STO π DRG› % Rnd Ran# A B C D E F X Y M ; e : CLR 1 3 . 2 ^ 3 2, 1 3 . 2 ^ 3 = 13.23 = © T Madas
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. EXP Ans = 1 2 3 + – 4 5 6 x ÷ 7 8 9 DEL AC RCL ENG ( ) , M+ (–) . , ,, hyp sin cos tan a b/c x2 log ln x-1 nCr Pol( REPLAY ^ SHIFT ALPHA MODE ON x! nPr Rec( x3 d/c 10x ex sin-1 cos-1 tan-1 M- OFF STO π DRG› % Rnd Ran# A B C D E F X Y M ; e : CLR 2 1 . 9 ^ 4 230, 2 1 . 9 ^ 4 = 21.94 = © T Madas
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© T Madas
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Calculate the following powers:
152 = 225 162 = 256 182 = 324 172 = 289 222 = 484 7.52 = 56.25 282 = 784 322 = 1024 12.52 = 156.25 252 = 625 4.52 = 20.25 0.162 = 0.0256 © T Madas
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Calculate the following powers:
55 = 3125 3052 = 93025 8.52 = 72.25 173 = 4913 123 = 1728 195 = 0.83 = 0.512 210 = 1024 2.12 = 4.41 = 1.952 = 3.8025 0.24 = 0.0016 © T Madas
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Calculate the following powers:
45 = 1024 1512 = 22801 73 = 343 153 = 3375 113 = 1331 163 = 4096 84 = 4096 38 = 6561 56 = 15625 67 = 279936 94 = 6561 216 = 65536 © T Madas
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© T Madas
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Calculate the following powers:
152 = 225 162 = 256 182 = 324 172 = 289 222 = 484 7.52 = 56.25 282 = 784 322 = 1024 12.52 = 156.25 252 = 625 4.52 = 20.25 0.162 = 0.0256 © T Madas
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Calculate the following powers:
55 = 3125 3052 = 93025 8.52 = 72.25 173 = 4913 123 = 1728 195 = 0.83 = 0.512 210 = 1024 2.12 = 4.41 = 1.952 = 3.8025 0.24 = 0.0016 © T Madas
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Calculate the following powers:
45 = 1024 1512 = 22801 73 = 343 153 = 3375 113 = 1331 163 = 4096 84 = 4096 38 = 6561 56 = 15625 67 = 279936 94 = 6561 216 = 65536 © T Madas
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© T Madas
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16 25 34 43 52 61 16 61 52 25 43 34 Look at the six numbers below.
Put them in order of size starting with the smallest. Circle the three square numbers Explain why 36 is a square number 16 25 34 43 52 61 16 61 52 25 43 34 16 = 1 x 1 x 1 x 1 x 1 x 1 = 1 25 = 2 x 2 x 2 x 2 x 2 = 32 4 8 16 34 = 3 x 3 x 3 x 3 = 81 9 27 43 = 4 x 4 x 4 = 64 16 52 = 5 x 5 = 25 61 = 6 © T Madas
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16 25 34 43 52 61 16 61 52 25 43 34 Look at the six numbers below.
Put them in order of size starting with the smallest. Circle the three square numbers Explain why 36 is a square number 16 25 34 43 52 61 16 61 52 25 43 34 36 = 3 x 3 x 3 x 3 x 3 x 3 = 27 x 27 © T Madas
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© T Madas
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