Chap 12 EXPONENTS AND POWERS

Chap 12

EXPONENTS AND POWERS

SOME IMPORTANT FACTS

1.      For any non-zero number a, b and positive integer m,n, we have ;

i)                    Aⁿ   = a x a x a x a x…………………n times.

ii)                  a^-n  = 1/aⁿ

iii)                a⁰   = 1

^iv)                                      a^m x aⁿ  = a ^m+n

v)                  a^m/aⁿ  = a ^m-n

vi)                (a^m)ⁿ  =  a ^mn  = (aⁿ)^m

vii)              (a x b)ⁿ  = aⁿ x bⁿ

viii)            (a/b)ⁿ  = aⁿ/bⁿ

2.      Exponential Equation :-

An equation having  an unknown quantity as an exponent is called an exponential equation.

To solve these equations the principle applied is that two numbers in exponential form with same base are equal only when exponent s are equal i.e. if a^m = aⁿ, then m = n.

3.      Standard Form :-

A number is said to be ion standard form if it is expressed as the product of a number between 1 and 10 and integral power of 10.