Power and Index

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  , is the base and 7 is the power

And
=
Remarks: In the exponential notation, the base can be any rational number and the power can be any integer.

Note: If the power of a rational number is 1 its value will be the rational number itself
i.e. (-10)1 = -10,  and in general
.

Example: Find the value of

Solution:

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 =       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 =
A negative integer as power
p-m =
other laws of exponents
pm x qm = (p x q)m

Few examples showing the application of laws of exponents.
Example1: Simplify (a)

Solution: a)

= 2-2 x 3-4+2 = 2-2 x 3-2

Example2: Find m if

Solution
(a) LHS=
RHS =
Equating LHS and RHS

Because base is same, powers must be equal
So -2m + 1 = -27
or -2m  = -27 – 1
= -28
or  m  = 14
(b) LHS =
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

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

The document Power and Index | Quantitative Techniques for CLAT is a part of the CLAT Course Quantitative Techniques for CLAT.
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## Quantitative Techniques for CLAT

56 videos|104 docs|95 tests

## FAQs on Power and Index - Quantitative Techniques for CLAT

 1. What is power in mathematics?
Ans. In mathematics, power refers to the operation of multiplying a number by itself a certain number of times. It is represented by an exponent, which indicates the number of times the base number is multiplied by itself.
 2. How do you calculate the value of a power?
Ans. The value of a power can be calculated by multiplying the base number by itself the number of times indicated by the exponent. For example, if the base number is 2 and the exponent is 3, the value of the power would be 2 x 2 x 2 = 8.
 3. What is an index or exponent in mathematics?
Ans. In mathematics, an index or exponent is a small number written above and to the right of a base number. It indicates the number of times the base number should be multiplied by itself. For example, in the expression 5^3, 3 is the exponent and 5 is the base number.
 4. How does the concept of power relate to real-life situations?
Ans. The concept of power is used in various real-life situations, such as calculating the area or volume of objects, determining the growth or decay of populations, analyzing financial investments, and understanding exponential growth or decay in natural phenomena.
 5. What are some common mistakes to avoid when working with powers and exponents?
Ans. When working with powers and exponents, it is important to avoid common mistakes such as forgetting to multiply the base number by itself the correct number of times, misinterpreting negative exponents, incorrectly applying the order of operations, and confusing exponentiation with multiplication or addition. Double-checking calculations and understanding the properties and rules of powers can help avoid these mistakes.

## Quantitative Techniques for CLAT

56 videos|104 docs|95 tests

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