Introduction to Exponents Video Lecture | Mathematics Olympiad Class 7

hello friends this video on exponents
and powers part 1 is brought to you by
exam for calm no more fear from exam
topics to be covered in this lesson our
introduction water exponents laws of
exponents multiply powers with same B's
divide powers with same ways power of a
power multiplied powers with same
exponents divide powers with same
exponents and decimal number system
large numbers and standard form a new
name for your right exponents and powers
so you might be wondering what could
exponents be so even before we talk
about exponents let us look at an
example it is look at a scenario from
our day-to-day life now if I ask you how
far is your school from your home so
assuming this is your home assuming this
is your home and this is your school so
if I ask you what is the distance
between your home and your school so you
might say that this distance could be
around maybe 10 kilometers it could be
15 kilometers at the max it could be
from 20 30 kilometers let's say that
this distance is 15 kilometers an
approximation now if I ask you now let's
say that both your home and your school
both of them are located in the same
city where you live so let's say that
you live in Bangalore now if I ask you
what is the distance between your city
that is Bangalore and Delhi
so that means right now I am basically
talking about this distance which is
definitely a lot larger than that of 15
kilometers so now this distance could be
somewhere around 117 hundred kilometers
so you see from 15 the value increased
to 1700 kilometers okay now both in
cities Bangalore and Delhi they are
in the same country that's India now if
I ask you how far is your country from
South America that is the distance
between India and South America so now I
am talking about this distance now this
distance could be as big as few 14900 15
kilometers so approximately 15,000
kilometers okay so we started with 15
then we had something around 1700 then
we have something around 15,000 now if I
tell you that how far is your planet
that is the earth so let's say this is
Earth and if I ask you how far is Earth
from the Sun so how much is this
distance so when you actually look at
this distance you see that it is 150
million kilometers now what is happening
in all of these examples you see we
started with a distance which was just
15 kilometers then we talked about a
distance which was 1700 kilometers then
we talked about a distance which was
approximately 15,000 kilometers and
finally we talked about a distance which
was 150 million kilometers so what is
happening so you see that for smaller
distances indicating them or
representing them with numbers like 15
or 1700 or even 15,000 is like decent
enough but when you talk about very big
numbers like 150 million so it's a huge
number and then you represent it like
this it becomes so confusing that how
many zeros are there because the zeros
will actually change the number if I
delete one zero it becomes 15 million
and there is a huge difference between
15 million and 150 millions so what is
happening here so with this we see that
it is very difficult to represent big
numbers as the numbers become bigger the
representation
becomes more complex so what is the role
of exponent the concept of exponents
make the representation of bigger
numbers easier that means
numbers like vids with seven zeroes
eight zeros ten zeros so these big
numbers can be very conveniently
represented using the concept of
exponents now here I have told you why
are you talking about exponents now when
we reach towards the end of this lesson
by when we will already know what is
exponent and how do we deal with it that
then I will actually show you that how
we can represent such big numbers using
exponents in a simpler way so the next
question is how exponent helps so let us
take a number for example so let us take
a smaller number for now let say we
consider one hundred now what does one
hundred how can you write hundred one
hundred can be written as 10 into 10
because 10 into 10 gives hundred right
so what are you actually doing so in
order to get 100 you are multiplying two
tens so when two tens are multiplied you
get a hundred so this concept of 10 into
10 can also be written as 10 to the
power 2 what does this mean this means
that we multiplied this number 10 two
times that means 10 into 10 so in a
similar way let's say that if I write n
to the power 3 what does that mean that
means that the number 10 is multiplied 3
times so 10 into 10 into 10 similarly 10
to the power 4 would mean the number 10
is multiplied 4 times now you see
instead of writing it as 10 into 10 into
10 into 10 it is easier to write it as
10 to the power 4 similarly if you write
10 to the power 10 so that actually
means that you are multiplying the
number 10 for 10 times so you see how
cumbersome is it is to you denote it by
writing tens so three four five six
seven eight nine and ten so this is how
you actually need to denote 10 to the
power 10 so these are more convenient
ways and this is the exponential form so
the exponential form of representing
1000 so 10 into 10 into 10 is 1,000 so
10 to the power 3 is the exponential
form of 1000 similarly 10 to the power 4
is the exponential form of 10,000 10 to
the power 10 again is exponential form
of this number so basically these are
all exponential form why are they
exponential form
what is the exponent there so when you
look at each of these numbers this
number is called the base and this
number which is raised to the power this
number is called exponent so in this
case what is the exponent 3 is the
exponent so in this case 4 is the
exponent here 10 is the exponent and
that is why these numbers are all
exponential form so you understand the
concept of exponents are now did you get
an idea that how exponent will help to
represent bigger numbers so when you
have a bigger number like this maybe 5 0
0 0 0 0 0 so here how many zeros do you
have 1 2 3 4 5 6 so this number can be
written as 5 into 10 to the power 6 so
instead of writing so many zeros you
just wrote 10 to the power 6 which means
that 10 gets multiplied 4 6 times and
then you also get the same number so
this is how exponent is going to help us
or it is going to make the
representation of bigger
numbers easier so that's the concept of
exponents so with this idea in mind
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