Introducing Powers © T Madas
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
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
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
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
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
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
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
The Square Numbers 1, 4, 9, 16, 25, 36, … 12 22 32 42 52 62 … © T Madas
© T Madas
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
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
© T Madas
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
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
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
© T Madas
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
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
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
© T Madas
Evaluate the following: 32 + 23 = 9 + 8 = 17 53 + 22 = 125 + 4 = 129 42 – 23 = 16 – 8 = 8 82 – 72 = 64 – 49 = 15 32 + 42 = 9 + 16 = 25 43 + 23 = 64 + 8 = 72 52 – 22 = 25 – 4 = 21 62 – 32 = 36 – 9 = 27 32 + 32 = 9 + 9 = 18 25 + 23 = 32 + 8 = 40 33 – 23 = 27 – 8 = 19 53 – 52 = 125 – 25 = 100 24 + 23 = 16 + 8 = 24 34 + 23 = 81 + 8 = 89 © T Madas
Evaluate the following: 42 + 23 = 16 + 8 = 24 53 + 32 = 125 + 9 = 134 52 – 23 = 25 – 8 = 17 92 – 72 = 81 – 49 = 32 62 + 42 = 36 + 16 = 52 82 + 33 = 64 + 27 = 91 72 – 32 = 49 – 9 = 40 102 – 32 = 100 – 9 = 91 42 + 42 = 16 + 16 = 32 26 + 23 = 64 + 8 = 72 33 – 24 = 27 – 16 = 11 43 – 42 = 64 – 16 = 48 25 + 24 = 32 + 16 = 48 34 + 43 = 81 + 64 = 145 © T Madas
© T Madas
Evaluate the following: 32 + 23 = 9 + 8 = 17 53 + 22 = 125 + 4 = 129 42 – 23 = 16 – 8 = 8 82 – 72 = 64 – 49 = 15 32 + 42 = 9 + 16 = 25 43 + 23 = 64 + 8 = 72 52 – 22 = 25 – 4 = 21 62 – 32 = 36 – 9 = 27 32 + 32 = 9 + 9 = 18 25 + 23 = 32 + 8 = 40 33 – 23 = 27 – 8 = 19 53 – 52 = 125 – 25 = 100 24 + 23 = 16 + 8 = 24 34 + 23 = 81 + 8 = 89 © T Madas
Evaluate the following: 42 + 23 = 16 + 8 = 24 53 + 32 = 125 + 9 = 134 52 – 23 = 25 – 8 = 17 92 – 72 = 81 – 49 = 32 62 + 42 = 36 + 16 = 52 82 + 33 = 64 + 27 = 91 72 – 32 = 49 – 9 = 40 102 – 32 = 100 – 9 = 91 42 + 42 = 16 + 16 = 32 26 + 23 = 64 + 8 = 72 33 – 24 = 27 – 16 = 11 43 – 42 = 64 – 16 = 48 25 + 24 = 32 + 16 = 48 34 + 43 = 81 + 64 = 145 © T Madas
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
. 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
. 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
. 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
. 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 2,299.968 1 3 . 2 ^ 3 = 13.23 = 2299.968 © T Madas
. 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 ^ 4 230,025.7521 2 1 . 9 ^ 4 = 21.94 = 230025.7521 © T Madas
© T Madas
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
Calculate the following powers: 55 = 3125 3052 = 93025 8.52 = 72.25 173 = 4913 123 = 1728 195 = 2476099 0.83 = 0.512 210 = 1024 2.12 = 4.41 1.0062 = 1.012036 1.952 = 3.8025 0.24 = 0.0016 © T Madas
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
© T Madas
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
Calculate the following powers: 55 = 3125 3052 = 93025 8.52 = 72.25 173 = 4913 123 = 1728 195 = 2476099 0.83 = 0.512 210 = 1024 2.12 = 4.41 1.0062 = 1.012036 1.952 = 3.8025 0.24 = 0.0016 © T Madas
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
© T Madas
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
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
© T Madas