Examples: Exponents basics Video Lecture - Class 7

hello friends this video on exponents
and powers part 4 is brought to you by
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based on the basics of exponents let us
now quickly look at some of the
questions question number 1 find the
value of 5 to the power of 4 now what do
we mean by 5 to the power 4 that means 5
is multiplied 4 times so this basically
means 5 into 5 into 5 into 5 so what
does this move this means 5 into 5 is 25
again 5 into 5 is 25 and 25 into 25 is
625 so the value of 5 to the power 4 is
625 question number to express the
following in exponential form so what is
the meaning of exponential form writing
something in the form of to the power so
here if you see a is getting repeated
for 3 times that is a is multiplied how
many times 3 times similarly C is
getting multiplied for 4 times and how
many times 4 D D is getting multiplied
only one time so that means a multiplied
for 3 times that is a to the power 3
into C multiplied for 4 times so C to
the power 4 and T multiplied 4 1 times 3
to the power 1 so D to the power 1 is
actually D because D multiplied only
once so this becomes equal to a cubed C
to the power 4 D so this would be the
answer question number 3 express the
following number using exponential
notation so here also we want to
represent 729 as some number to the
power some number so in that form we
want to represent 729 so for that what
do we need to do so the first thing that
we will do is prime factorization of 729
only then we will get to know like how
we can represent 729 in the form of its
prime factors so this is 729 so let us
first start with the smallest prime
number which is 2 but 2 doesn't divide
729 exactly so let's move on to the next
prime number that is 3 now 3 divides it
exactly 3 to the 6 3 4 12 3 threes and 9
now this 214 43 is again completely
divisible by 3 so 3 eights are pending
for 3 ones or 3 again three twos are six
three sevens a 21 again three nines or
27 3 threes or 9 so this is how we can
prime factorize 729 so we can write 729
is equal to 3 into 3 into 3 into 3 into
3 so this is what we can write 3 in 3
into 3 3 into 3 into 3 so basically how
many times three is getting repeated it
is getting repeated 4 6 times so this
can be written as 3 to the power 6 so
729 can be written as 3 to the power 6
so this is the exponential notation
question number 4 identify the greater
number wherever possible in each of the
following so in the first case we have 5
to the power 3 so 5 to the power 3 would
mean 5 multiplied 3 times that is 5 into
5 into 5 which is equal to 125 what is
the meaning of 3 to the power 5 that
means 3 is getting multiplied for 5
times so 3 into 3 into 3 into 3 into 3
so 3 3 is a 990 is a 27 and then this 3
threes are nice
27 in 9 this is equal to 243 now if you
compare 243 with 125 what do you see you
see that 243 is greater than 125
therefore 3 to the power 5 is greater
than 5 to the power 3 now let us look at
the second one 100 to the power 2 and 2
to the power 100 so let us first look at
100 to the power T so hundred to the
power 2 would be hundred in 200 which is
equal to 110 thousand let us thank to
the power for later
10,000 is the one now it is look at two
to the power hundred so 2 to the power
hundred actually means 2 is getting
multiplied for how many times 400 times
so do you think it is possible to write
down to 400 times that is little
unfeasible so what we will do instead of
writing it 400 times let us try to write
it for 10 times so if you multiply 2 for
10 times how much what is the value that
you get 2 2 so 4 4 2 2 8 into 16 then
again you have these many twos so 16 is
a 32 32 into 2 is 64 64 into 2 is 128
128 into 2 is 256 256 into 2 is so in
this way we find that 2 multiplied for
10 times gives us 1 0 2 4 now here we
have to multiply it 400 times that means
if we divide that hundred times into 10
10 times each so 10 twos together again
10 tools together again
who's together so if we divide it like
this into group so how many groups we
will have we will have 1 2 3 4 5 6 7 8 9
and 10 groups so when you have 10 twos
in each group so in 10 groups how many
twos you will have 100 right so that
means this one 0 2 4 will basically get
multiplied for 10 times now tell me do
you think that such a big number a
four-digit number getting worse be
flying for 10 times so the result that
you will get is going to be a huge
number which will definitely be a lot
greater than 10,000 so therefore we can
say that 2 to the power hundred will be
greater than 100 to the power 2 so I
hope you understood this logic right so
instead of multiplying to 400 times we
divided twos into groups of 10 so in
each group we have ten twos now the
product of 10 to s is equal to 1 0 to 4
so how many 1 0 to 4 we have we have 10
1 0 2 4 so looking at that we can say
that 2 to the power hundred is greater
question number 5 simplify 3 to the
power 2 multiplied it by 10 to the power
4 so 3 to the power 2 would be nothing
but 3 into 3 that is 9 and what about 10
to the power 4 that is nothing but 10
into 10 into 10 into 10 which gives
10,000 so when you actually find their
product that is 3 to the power 2 into 10
to the power 4 is equal to 9 into 10,000
so this is equal to 90,000 question
number 6 simplify minus 2 to the power 3
multiplied by minus 10 to the power 3 so
minus 2 to the power 3 that means minus
2 into minus 2 into minus 2 now whenever
you
find product of negative numbers one
simple tip that you remember is first
you find the product irrespective of the
sign irrespective of the negative sign
so in this case two twos are four twos
are eight so the product is eight in
this case now whether this product would
be positive or negative that depends on
how many times the negative sign is
getting repeated so here how many times
you see negative sign one two three so
if you have the negative sign for odd
number of times like if the negative
sign is there for one time or three
times or five times or seven times in
that case that result would be negative
if the negative sign exists for even
number of times like two four six or
eight in that case the result would be
positive so we have discussed about all
these things in the basic mathematics
but still I am repeating it here now let
let's do with the same thing for minus
10 to the power 3 in this case again you
have minus 10 into minus 10 into minus
10 you are also follow the same
technique first find the product with
respective of the signs and 10 into 10
into 10 would be thousand and the result
would be negative or positive so here
also you have how many times negative
sign 3 times so 3 is odd-numbered
therefore the result would be negative
so now in the question if C is minus 2
to the power 3 multiplied by minus 10 to
the power 3 so minus 2 to the power T is
minus 8 and minus 10 to the power 3 is
minus 1,000 now when you find this
product here also follow the same
technique first find the product
irrespective of the sign which is 8000
now here how many times you have
negative sign
2 times 2 is an even number therefore
the result would be positive so 8000
good reader
answer question number 7 compare the
following numbers 4 into 10 to the power
14 or 3 into 10 to the power 17 now here
if you look at it the first number here
it is 4 and here it is 3 so 4 is greater
than 3 it's obvious but when you look at
the second number you see here it is
to the power 14 so 10 to the power 14
means after 4 you will have 14 zeros
when you say 10 to the power 17 that
means after 3 this number will have 17 0
something like this so after 4 you have
14 zeros but in the second number how
many zeros you have 17 zeros now look at
these two numbers which one do you think
is greater obviously the one with more
number of zeros because the moment you
increase the zeros you are actually
increasing the value of the number a lot
you increase one zero in 10 it becomes
100 you increase one more zero to the
hundred it becomes thousand you increase
one zero two thousand it becomes ten
thousand so you are adding one zero
makes a lot of difference so in this
case since the number of zeros is more
in the second number therefore 3 into 10
to the power 17 is greater than 4 into
10 to the power 14 you always want me to
write the number putting all the zeros
while I did this was district 10 just to
show you that how 3 into 10 to the power
17 is greater than 4 into 10 to the
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