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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