How to solve “exponents” and exponent rules.

EXPONENTS AND THEIR RULES

Here I have a topic to explain i.e. “ EXPONENTS AND THEIR RULES.”
Hope you have gone through my previous articles
How did you feel, What Improvement you want, What questions and queries you have?

let’s get started…

first of all I let you introduce with the

rules of exponents :-

any term which is having any exponents is called as base and rules varies with the behaviour of functions like Additions, Subtractions, Multiplications & Divisions.

Term:- Base with some exponents known as term,
so when two terms are added with same or different exponents will not be added until the terms which are given in numbers or numeric digits, and should not be in variables
but, do remember even if these are numbers (base and  in exponents) also though we have to solute those terms individually​ (same rules will be applied for terms with exponents are in subtraction) for e.g.
2² + 3³
now in this they can’t be added because of BODMAS RULE,
according to this first of all Brackets then orders will be solved and after it other functions be solved,
now continue with solution proceed
=2² ± 3³

=8  ± 9

=17 or -1
again if ,

=2² ± 2⁴

this can’t be written as 2 raise to power 6
so, How this would be solved?
by following the rule of exponents

=4 ± 16

= 20 or -12
if it is in variables like

x² ± y³

then it will remain as it is until the values of variables are given.
Rules for Multiplication and division:-

If terms are in multiplication then it will be solved again by applying BODMAS RULE
but there is a bit difference i.e.

if the (terms are in multiplications) base are same then exponents will be added.
=x² × x³

= x ³+²

= x5
and if the base are different then exponents (will remain same and solved individually) can’t be added.
=2² × 3³

= 4× 27

= 108
Now when it comes to Division,
if the base are same then exponents will be subtracted (Basic Concept) i.e.
if any number or variable lies at denominator with some exponents to solve the fraction from denominator we’ll have to bring the term at numerator in this process we’ll have to change the sign of exponents i.e. for e.g.

=x² / x³

= x ² – ³

= x౼¹
to make it positive exponent
this term will move into denominator
= 1/x
But if the base are different then it will remain same as usual.
I want to add here one more concept i.e.
if any base is having exponent’s exponent, for solution of those terms exponents will be multiplied you all can have a look at third rule in following image
For summarising the whole article I have comprises all the exponent rules in following pic
:-
you can go through by taking some examples.
Now it’s your turn tell me what doubts yo are still facing and if you have any query then please comment under the comment box.