Assignment 1 Solutions

# Assignment 1 Solutions - Assignment#1 1 What is 5 25 125...

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Assignment#1 1. What is 5 · 25 · 125 · 625 · 3125 · 15625 · 78125 · 390625 · 1953125 · 9765625 · 48828125 · 244140625 · 1220703125? 5 1 · 5 2 · · · 5 12 · 5 13 5 1+2+ ··· +12+13 5 91 2. Rationalise 2+ 3 2 - 3 . 2 + 3 2 - 3 2 + 3 2 - 3 2 + 3 2 + 3 (2 + 3) 2 2 2 - 3 2 4 + 4 3 + 3 4 - 3 7 + 4 3 3. If n = m 5 and m 2 = 7, what is n 3 · m ? n 3 · m ( m 5 ) 3 · m m 15 · m m 16 ( m 2 ) 8 7 8

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4. If x 3 y 5 = 2 11 · 3 13 and x y 2 = 1 27 , solve for x and y . Rearrange the second equation. x y 2 = 1 27 x = y 2 27 Sub x = y 2 27 into the first equation. x 3 y 5 = 2 11 · 3 13 y 2 27 3 y 5 = 2 11 · 3 13 ( y 2 ) 3 27 3 y 5 = 2 11 · 3 13 ( y 6 ) (3 3 ) 3 y 5 = 2 11 · 3 13 ( y 6 ) 3 9 y 5 = 2 11 · 3 13 y 11 = 3 9 · 2 11 · 3 13 y 11 = 2 11 · 3 22 y 11 = (2 · 3 2 ) 11 y = 2 · 3 2 = 18 Sub y = 2 · 3 2 into the second equation. x y 2 = 1 27 x = y 2 27 x = (2 · 3 2 ) 2 27 x = 2 2 · 3 4 3 3
x = 2 2 · 3 4 - 3 x = 2 2 · 3 1 = 12 5. Solve for x : 2 8 x = 16 2 2 2 (2 3 ) x = (2 4 ) 2 2 2 2 3 x = 2 4 · 2 2 2 3 x = 4 · 2 2 2 3 x = 2 2 · 2 2 2 3 x = 2 4 3 x = 4 x = 3 4 If you decided not to use the corrected version, here is that solution: 2 8 x = 16 2 x 2 (2 3 ) x = (2 4 ) 2 x 2 2 3 x = 2 4 · 2 x 2 3 x = 4 · 2 x 2 3 x = 2 2 · 2 x 2 3 x = 2 2+ x 3 x = 2 + x 2 x = 2 x = 1 6. Simplify: a b + b a + 2 a + b 2 a - b a - b ÷ h a + 2 b + b 2 a a a + b + b a - b i

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a 2 + b 2 + 2 ab ab ( a + b )( a - b ) - 2 ab 2 a ( a - b ) ÷ h a 2 + 2 ab + b 2 a a ( a - b ) + b ( b + a ) ( a + b )( a - b ) i ( a + b ) 2 ab a 2 - b 2 - 2 ab 2 a ( a - b ) ÷ h ( a + b ) 2 a a 2 - ab + b 2 + ab ) ( a + b )( a - b ) i ( a + b ) 2 ab a 2 - b 2 - 2 ab 2 a ( a - b ) ÷ h ( a + b ) 2 a a 2 + b 2 ( a + b )( a - b ) i ( a + b ) 2 ( a 2 - b 2 - 2 ab ) 2 a 2 b ( a - b ) ÷ h ( a + b ) 2 ( a 2 + b 2 ) a ( a + b )( a - b ) i ( a + b ) 2 ( a 2 - b 2 -
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