Ratio and Proportion, Indices and Logarithm

CPT Section D Quantitative Aptitude Chapter 1 Part III: Indices

Ms. Ritu Gupta MA (Maths)

Indices

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Learning Objectives

Meaning of Indices and

their Application

Laws of Indices which

facilitates their easy

applications

Laws of Surds

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Indices

If a is a non-zero real number and n is a positive integer, then

a X a X a X …………………… n times is represented as an where, a is called the base and n is called the exponent or power or index.

Similarly (a X a X a X …………………… n times) (b X b X b X ………………… m times) will be represented as anbm

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Laws of Indices

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Laws of Indices- Continued

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Surds

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Equality Of Surds

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Laws of Surds

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Laws of Surds - Continued

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Results

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Identities

(a +b)2 = a2 + b2 + 2ab

(a -b)2 = a2 + b2 - 2ab

(a +b) (a-b) = a2 – b2

(a+b+c)2 = a2 + b2 + c2 +2ab + 2bc +2ca

(a + b)3 = a3 + b3 + 3ab (a+b) or

(a + b)3 = a3 + b3 + 3a2b +3ab2

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Identities - Continued

(a – b)3 = a³ - b³- 3ab(a – b) or

(a – b)3 = a³ - b³- 3a²b + 3ab²

a³ + b³ = (a+b) (a² - ab + b²)

a³ - b³ = (a-b) (a² + ab + b²)

Note: If we want to find a² + b²

Then we know (a+b)² = a² + b² + 2ab

a² + b² = (a+b)² - 2ab

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Illustrations

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Illustration 1

Simplify: 32 × (8)-4/3

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Solution: 32 × (8)-4/3 = 25 × (2³)-4/3 = 25 × (2)-4 = 25-4 = 2

Illustration 2

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Illustration 3

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Illustration 3 - Continued

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Illustration 4

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Illustration 4 - Continuded

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Illustration 4 - Continuded

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Illustration 5

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Illustration 6

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Illustration 6 - Continued

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Illustration 7

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Illustration 8

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Illustration 9

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Illustration 9 - Continued

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Illustration 10

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Illustration 10 - Continued

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Illustration 11

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Illustration 11 - Continued

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Illustration 12

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Illustration 13

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Illustration 14

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Illustration 14 - Continued

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THANK YOU

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