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Powers of Real Numbers(Exponents),[object Object]
Exponents represent repeated multiplication. For example,,[object Object],Introduction ,[object Object]
More generally, for any non-zero real number a and for any whole number n,,[object Object],Introduction ,[object Object],In the exponential expression an, a is called the base and n is called the exponent.,[object Object]
a2 is read as ‘a squared’.,[object Object],a3 is read as ‘a cubed’.,[object Object],a4 is read as ‘a to the fourth power’.,[object Object],   ...,[object Object],an is read as ‘a to the nth power’.,[object Object]
Caution!,[object Object]
Caution!,[object Object]
Properties of Exponents,[object Object]
Example:,[object Object]
Properties of Exponents,[object Object]
Example:,[object Object]
Properties of Exponents,[object Object],Homework.,[object Object]
Example:,[object Object]
Some Definitions of Exponents,[object Object]
Properties of Exponents,[object Object],Homework.,[object Object]
Example:,[object Object]
Properties of Exponents,[object Object],Homework.,[object Object]
Example:,[object Object]
Properties of Exponents,[object Object],Homework.,[object Object]
Example:,[object Object]
Properties of Exponents,[object Object],All powers of a positive real number a are positive, i.e. for a ∈ R, a > 0, and n ∈ Z,,[object Object],an > 0. ,[object Object],2. The even powers of a negative real number a are positive, i.e. for a ∈ R, a ≠ 0 and n ∈ Z,,[object Object],(–a)n = an (if n is an even number).,[object Object],3. The odd powers of a negative real number a are negative, i.e. for a ∈ R, a ≠ 0 and n ∈ Z,,[object Object],(–a)n= –an (if n is an odd number),[object Object]
Example:,[object Object]
Example:,[object Object]
Properties of Exponents,[object Object],    The terms of an expression which have the same base and the same exponent are called like terms. We can add or subtract like terms.,[object Object],(x ⋅ an) + (y ⋅ an) + (z ⋅ an) = (x + y + z) ⋅ an            (a ≠ 0),[object Object]
Example:,[object Object]
Let a ∈ R – {–1, 0, 1} ,[object Object],(a is a real number other than –1, 0 and 1).,[object Object],        If am = an then m = n.,[object Object],Exponential Equations,[object Object]
2x = 16,[object Object],3x+1 = 81,[object Object],22x + 1 = 8x – 1,[object Object],Examples:,[object Object]
Exercises:,[object Object]

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