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Arithmetic – Exponents
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Exponent
• Shorthand for repeated multiplication of same number by itself.
• E.g: 2 * 2 * 2 * 2 = 24. Where 2 is called as base and 4 is called as Exponent.
• Xy is also called X power of Y. where X is the base and Y is the
exponent.
• X2 is called as X square
• X3 is called as X cube
• X4 is called as X Power 4
• X0 = 1 [where x is any integer or decimal]
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Exponents Formula
• Formula 1: (Xm) (Xn) = Xm+n
• E.g: 23 * 24 = 27 . Proof ?
2*2*2 * 2*2*2*2 = 128
27 = 128.
• In Multiplication, if bases are equal powers should be added.
• Formula 2: (Xm)/(Xn) = Xm-n
• E.g: 24 / 23 = 21 . Proof ?
(2*2*2*2) / (2*2*2) = 2
21 = 2.
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Exponents Formula
• Formula 3: (Xm)n = Xm*n
• E.g: (22)3 = 26 . Proof ?
22 * 22 * 22 = 2(2+2+2) = 26 [Formula 1]
• Formula 4: (Xm/n) = n√Xm
• E.g: (43/2) = 8. Proof ?
43/2 = 43*1/2 = (43)1/2 [Formula 3]= (64)1/2 = 8
• Note: √X can also be written as X1/2
• Formula 5: (X-m) = 1/Xm
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Example Problems
• Quantity A: -24
Quantity B: (-2)4
Ans: Quantity B
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Example Problems
• Convert 4-6 into positive power of 8?
• Given number 4-6
= (22)-6
= 22*-6
= 22*-3*2
= 23*-2*2
= (23 ) -4
= (8)-4
= 1/84
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Example Problems
• What is the value of (X1/3)12?
= (X1/3*12)
= (X4)
• What is the value of (2Y2/3)6
= 26 * (X2/3)6 [ (XY)n = Xn * Yn ]
= 64 * X4
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Example Problems
• Quantity A: 54 + 55
Quantity B: 53 + 56
Sol:
Quantity A: 53 ( 5 + 52 )
= 125 * (30)
Quantity B: 53 ( 1 + 53 )
= 125 * (126)
Ans: B
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Example Problems
• Given 4x+1 = 256 , what is the value of 4x + 1 ?
Sol: 4x+1
4x * 4 = 256
4x = 64
4x = 43
Hence x = 3
Value of 4x + 1 = 65
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Example Problems
• (0.0025*10x)/(500*10-4) = 0.5 * 103 . What is the value of x?
Sol:
Ans: x = 4
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Example Problems
• Find the value of 5k – 5k+1 + 5k-1 ?
Ans: 19 * 5k-1
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Contact Information
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• Slideshare: http://www.slideshare.net/GREQuantWorld
• Email Address: grequantworld @ gmail.com
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