Quick Revision Notes For CPT - Index Numbers

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CPT Maths - Index Numbers Revision Notes

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UNDERSTANDING INDEX NUMBERS:

To understand Index Numbers we tack up certain higher order operations with power & roots under the respective heads of indices. e.g.

9 x 9 x 9 x 9 x 9 x 9 = 9⁶
a x a x a x a x a x a = a⁶

In all such cases a factor which multiplies is called the “Base” and the number of times it is multiplied is called the “Power” or the “Index”. Therefore, “9” and “a” are the bases and “6” is the index or power for both.

Rules of Indices:

1. a^m x aⁿ = a^m+n (base must be same) e.g. 5³ x 5⁴ = 5³⁺⁴ = 5⁷
2. a^m / aⁿ = am-n (base must be same) e.g. 5⁷ / 5⁴ = 5^7-4 = 5³
3. (a^m)ⁿ = a^mn where m and n are positive integers.
4. (ab)ⁿ = aⁿ.bⁿ when n can tack all values.
5. a⁰ = 1
6. a¹ = a
7. 1ⁿ = 1
8. a^-m = 1/a^m
9. ^m√a = a^1/m
10. if a^x = a^y, then x = y
11. if x^a = y^a, then x = y
12. if a^x = b^x and a ≠ b, then x = 0.

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