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1. Ratio and Proportion,
Indices and Logarithm
CPT Section D Quantitative Aptitude Chapter 1
Part III: Indices
Ms. Ritu Gupta MA (Maths)

2. Indices
2

3. Learning Objectives
Meaning of
Indices and
their
Application
Laws of
Indices
which
facilitates
their easy
applications
Laws of
Surds
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4. 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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5. Laws of Indices
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6. Laws of Indices- Continued
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7. Surds
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8. Equality Of Surds
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9. Laws of Surds
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10. Laws of Surds - Continued
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11. Results
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12. 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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13. 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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14. Illustrations
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15. 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

16. Illustration 2
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17. Illustration 3
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18. Illustration 3 - Continued
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19. Illustration 4
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20. Illustration 4 - Continuded
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21. Illustration 4 - Continuded
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22. Illustration 5
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23. Illustration 6
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24. Illustration 6 - Continued
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25. Illustration 7
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26. Illustration 8
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27. Illustration 9
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28. Illustration 9 - Continued
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29. Illustration 10
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30. Illustration 10 - Continued
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31. Illustration 11
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32. Illustration 11 - Continued
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33. Illustration 12
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34. Illustration 13
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35. Illustration 14
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36. Illustration 14 - Continued
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37. THANK YOU
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