Power and Index Quant Notes | EduRev

Quantitative Techniques for CLAT

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Quant : Power and Index Quant Notes | EduRev

The document Power and Index Quant Notes | EduRev is a part of the Quant Course Quantitative Techniques for CLAT.
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Chapter 2 Power and Index  

In pn, p is called the base and n is called the power or index
In (-5)7, -5 is te base and 7 is the power
In Power and Index Quant Notes | EduRev ,Power and Index Quant Notes | EduRev is the base and 7 is the power
Power and Index Quant Notes | EduRev   
Power and Index Quant Notes | EduRev
And Power and Index Quant Notes | EduRev
= Power and Index Quant Notes | EduRev
Remarks: In the exponential notation, the base can be any rational number and the power can be any integer.
Power and Index Quant Notes | EduRev
Note: If the power of a rational number is 1 its value will be the rational number itself
i.e. (-10)1 = -10, Power and Index Quant Notes | EduRev and in general
Power and Index Quant Notes | EduRev . 

Example: Find the value of
 Power and Index Quant Notes | EduRev
Solution: Power and Index Quant Notes | EduRev
Power and Index Quant Notes | EduRev
Power and Index Quant Notes | EduRevPower and Index Quant Notes | EduRev
Power and Index Quant Notes | EduRev
Power and Index Quant Notes | EduRev
Product law for exponents: If p is a non-zero rational number and m and n are two positive integers then pm x pn = p m+n
also pm x pn x pr x ps = pm+n+r+s
also (pm)n = pmn

Quotient law for exponents: It p is a non- zero rational number and m and n are two positive integers
then pm ÷   pn = pm-n   for m > n
and pm ÷ pn =  Power and Index Quant Notes | EduRev     for m < n

If power is zero (o): If p is a non-zero rational number then po = 1
If power is (-1): If p is a non-zero rational number then p-1 denotes the reciprocal of p and (p)-1 = Power and Index Quant Notes | EduRev
A negative integer as power
p-m = Power and Index Quant Notes | EduRev
other laws of exponents
pm x qm = (p x q)m
 Power and Index Quant Notes | EduRev

Few examples showing the application of laws of exponents.
Example1: Simplify (a) Power and Index Quant Notes | EduRev
Power and Index Quant Notes | EduRev
Solution: a) Power and Index Quant Notes | EduRev
Power and Index Quant Notes | EduRevPower and Index Quant Notes | EduRev
Power and Index Quant Notes | EduRev
Power and Index Quant Notes | EduRev
Power and Index Quant Notes | EduRev
= 2-2 x 3-4+2 = 2-2 x 3-2
Power and Index Quant Notes | EduRev

Example2: Find m if
Power and Index Quant Notes | EduRev
Power and Index Quant Notes | EduRev

Solution
(a) LHS= Power and Index Quant Notes | EduRev
RHS = Power and Index Quant Notes | EduRev
Equating LHS and RHS
 Power and Index Quant Notes | EduRev
Because base is same, powers must be equal
So -2m + 1 = -27
or -2m  = -27 – 1
= -28
or  m  = 14
(b) LHS = Power and Index Quant Notes | EduRev
RHS = 2m
So 2m = 25
Or m = 5.

Example: Solve for x
a) 3x = 81              b) (72x)-2 = (2401)
-1

Solution a) RHS = 81 = 34
So 3x = 34 or x = 4
Solution b) RHS= (2401)-1 = (74)-1 = 7-4
LHS = (72x)-2 = 7-4x
Equating LHS and RHS
7-4X = 7-4
Base in same, powers must be equal
-4x = -4
Or  x = 1

What is the difference between exponents
Power and Index Quant Notes | EduRev
Power and Index Quant Notes | EduRev = pm x pm x pm x pm --------- n times
 =pm+m+m+m ------ n times
=pm n
Where as Power and Index Quant Notes | EduRev= Power and Index Quant Notes | EduRev
Let us simplify it with the help of an example
Find the difference between Power and Index Quant Notes | EduRev
(22)3 = 22 x 22 x 22 = 26
Power and Index Quant Notes | EduRev  = 22x2x2 = 28
So the diff. is very clear.

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