Class 7 Exam > Class 7 Videos > L7 : Questions - Exponents and Powers, Mathematics, CBSE Class 7
L7 : Questions - Exponents and Powers, Mathematics, CBSE Class 7 Video Lecture
FAQs on L7 : Questions - Exponents and Powers, Mathematics, CBSE Class 7 Video Lecture
| 1. What is an exponent? |  |
Ans. An exponent is a number that represents the power to which another number, called the base, is raised. It tells us how many times the base is multiplied by itself.
| 2. How do you read and write exponents? | |
Ans. Exponents are read as "base raised to the power of the exponent." For example, 2^3 is read as "2 raised to the power of 3." When writing exponents, the base is written first, followed by the exponent as a superscript.
| 3. What is the difference between an exponent and a power? | |
Ans. An exponent is a single number that represents the power to which a base is raised, whereas a power refers to the entire expression that includes the base and the exponent. For example, in 2^3, 3 is the exponent and 2^3 is the power.
| 4. How do you calculate the value of an exponent? | |
Ans. To calculate the value of an exponent, you can simply multiply the base by itself the number of times equal to the exponent. For example, to find the value of 2^3, you would multiply 2 by itself three times (2 x 2 x 2 = 8).
| 5. What are the rules of exponents? | |
Ans. There are several rules of exponents, such as the product rule (a^m * a^n = a^(m+n)), the quotient rule (a^m / a^n = a^(m-n)), and the power rule ((a^m)^n = a^(m*n)). These rules help simplify calculations and manipulate expressions involving exponents.
Text Transcript from Video
hello friends this video on exponents
and powers part 7 is brought to you by
exam for calm no more fear from exam so
based on these laws of exponents let us
have a look at some of the questions
question number 1 using laws of
exponents simplify and write the answer
in exponential form so the first one is
a to the power 4 multiplied by B to the
power 4 so in this case you have
different bases a and B but you have the
same exponent that is 4 so what will
happen in this case your ways would be
the product of a and B and what would be
the exponent this will definitely be 4
so a B to the power 4 would be the
answer second one 2 to the power 20
divided by 2 to the power 15 so if you
look at these two they have the same
base but different exponents so when you
divide these two your base will be 2 but
what about the exponent so that way they
will get subtracted because here the
numbers are getting divided so 2 to the
power 20 minus 15 into 2 to the power 3
so this would be 2 to the power 5 into 2
to the power 3 in this case again you
have same base but different exponents
this time you are multiplying so the
powers will get added so the answer
would be 2 to the power 8 question
number 2 simplify and express each of
the following in exponential form the
first one a to the power 5 by a to the
power 3 into a to the power 8 so let us
first sort the denominator out so in the
denominator you have a to the power in
the numerator you have a to the power 5
multiplied by a to the power 8 so a to
the power 5 Plus 8 and what do you have
in the denominator you have a to the
power 3 so this is equal to 8 plus 5 is
13 and here it is 3 so now you have
division with same base but different
exponents so the exponents will get
subtracted so you get the answer as
a to the power 10 let's look at the
second one 3 into 7 square into 11 to
the power 8 divided by 21 into 11 to the
power 3 now you see here we have 3 & 7
in the numerator now if you observe the
denominator closely you see that 21 can
be very well written as 3 into 7 because
3 into 7 is 21 so now what do you see
you have got similar bases in the
numerator and denominator so what we
would do is first let us sort out 3 so 4
3 here you have 1 here also you have 1
so the powers will get subtracted
because it is division right so this
multiplied by 7 so again in 7 or 2 the
powers will get subtracted then 11 there
also the powers get subtracted so 3 to
the power 0 into 7 to the power 1 11 to
the power 5 so anything to the power 0
is 1 so 1 into 7 into 11 to the power 5
so this is equal to 7 into 11 to the
power 5 question number 3 stakes a true
or false and justify your answer 2 to
the power 3 is greater than 5 to the
power 2 so let us see how much would be
the value of 2 to the power 3 so 2 to
the power 3 would be 2 into 2 into 2
which is equal to 8 and what about 5 to
the power 2 so 5 square would be nothing
but 5 into 5 that is 25 now here we very
clearly see that 25 is greater than 8
therefore 5 square it should be greater
than 2 to the power 3 but in this case
it says 2 to the power 3 is greater than
5 square that means this is false next
one 3 to the power 0 is equal to 1000 to
the power 0 this is absolutely true
that's because anything to the power 0
is equal to 1 so both of these equal to
1 question number 4 expressed as a
product of prime factors only in
exponential form so
in here also whenever you have to
express as product of prime factors the
first thing that you need to do is fly
in factorization so when you do prime
factorization of 729 you see that it is
totally divisible by 3 again 243 is also
divisible by 3 so this is 27 then 3 9 27
3 3 9
therefore 729 can be written as 3 into 3
into 3 into 3 into 3 into 3 so this can
be written as 3 to the power 6 because 3
is getting multiplied 6 times in a
similar way we will do it for 64 so this
is 2 3 is a 6 to 2 so 4 to 16 or 32 2 8
16 2 4 8 2 2 so 4 so 64 is equal to 2
into 2 into 2 into 2 into 2 so again 2
is getting multiplied for 6 times so
this is equal to 2 to the power 6
therefore when you look at the final
product which is 729 into 64 this is
equal to 3 to the power 6 into 2 to the
power 6 so we have successfully
expressed this as product of prime
factors in exponential form so here 2 &
3 are the prime factors question number
5 simplifying 25 into v square into T to
the power 8 divided by 10 cube into 10
to the 8th e to the power 4 so here you
know wherever we have to simplify things
related to exponents our target is
always to convert them either into same
bases with different exponents or
different bases with same exponents so
that is what we target at so in this
case we cannot do anything with the
exponents but we can play around with
the bases for example we can write 25 as
5 into 5 so what happens you get same
base in all of these right similarly in
the denominator you can
right 10 as 2 into 5 so this becomes 2
into 5 to the power 3 into T to the
power 4 so you have a lot of numbers
where the base is fine so now let's see
so now in the numerator you consider the
three of these so here it is 1 here also
it is 1 so 5 to the power 1 plus 1 plus
2 into T to the power 8 divided by so 2
into 5 to the power 3 so what does that
mean so that can be written as 2 to the
power 3 into 5 to the power 3 into T to
the power 4 so this is 5 to the power 4
into T to the power 8 divided by 2 to
the power 3 what would be the value 2 to
the 4 4 to 8 so this would be 8 into 5
to the power 3 into T to the power 4 now
here you see this descendants they have
the same DS so it becomes 5 to the power
4 minus 3 because this is division
similarly T to the power 8 minus 4
because both again these two are
division and this divided by 8 so this
would be 5 to the power 1 into T to the
power 4 divided by 8 so this can be
written as 5 by 8 T to the power 4 so
this would be the answer so you see this
is the technique of simplifying
exponents so whenever you have exponents
all this try and target at making the
bases equal so if you have same bases
then you can apply the laws of exponents
and the entire problem gets very much
simplified now if you had not used the
law of exponents in that case you would
have actually been doing 5 into 5 25 25
into 25 6 25 so you would have been
doing those calculations which was
absolutely not needed thank you please
visit exam fee or come for free quality
education you can learn with a simple
four-step learning process wherein you
can watch video lessons you can ask your
questions you can refer notes and you
can take a free
online test we have content for class
six to twelve on physics chemistry
mathematics and biology along with
practical videos so please subscribe to
our channel for daily updates thank you
and powers part 7 is brought to you by
exam for calm no more fear from exam so
based on these laws of exponents let us
have a look at some of the questions
question number 1 using laws of
exponents simplify and write the answer
in exponential form so the first one is
a to the power 4 multiplied by B to the
power 4 so in this case you have
different bases a and B but you have the
same exponent that is 4 so what will
happen in this case your ways would be
the product of a and B and what would be
the exponent this will definitely be 4
so a B to the power 4 would be the
answer second one 2 to the power 20
divided by 2 to the power 15 so if you
look at these two they have the same
base but different exponents so when you
divide these two your base will be 2 but
what about the exponent so that way they
will get subtracted because here the
numbers are getting divided so 2 to the
power 20 minus 15 into 2 to the power 3
so this would be 2 to the power 5 into 2
to the power 3 in this case again you
have same base but different exponents
this time you are multiplying so the
powers will get added so the answer
would be 2 to the power 8 question
number 2 simplify and express each of
the following in exponential form the
first one a to the power 5 by a to the
power 3 into a to the power 8 so let us
first sort the denominator out so in the
denominator you have a to the power in
the numerator you have a to the power 5
multiplied by a to the power 8 so a to
the power 5 Plus 8 and what do you have
in the denominator you have a to the
power 3 so this is equal to 8 plus 5 is
13 and here it is 3 so now you have
division with same base but different
exponents so the exponents will get
subtracted so you get the answer as
a to the power 10 let's look at the
second one 3 into 7 square into 11 to
the power 8 divided by 21 into 11 to the
power 3 now you see here we have 3 & 7
in the numerator now if you observe the
denominator closely you see that 21 can
be very well written as 3 into 7 because
3 into 7 is 21 so now what do you see
you have got similar bases in the
numerator and denominator so what we
would do is first let us sort out 3 so 4
3 here you have 1 here also you have 1
so the powers will get subtracted
because it is division right so this
multiplied by 7 so again in 7 or 2 the
powers will get subtracted then 11 there
also the powers get subtracted so 3 to
the power 0 into 7 to the power 1 11 to
the power 5 so anything to the power 0
is 1 so 1 into 7 into 11 to the power 5
so this is equal to 7 into 11 to the
power 5 question number 3 stakes a true
or false and justify your answer 2 to
the power 3 is greater than 5 to the
power 2 so let us see how much would be
the value of 2 to the power 3 so 2 to
the power 3 would be 2 into 2 into 2
which is equal to 8 and what about 5 to
the power 2 so 5 square would be nothing
but 5 into 5 that is 25 now here we very
clearly see that 25 is greater than 8
therefore 5 square it should be greater
than 2 to the power 3 but in this case
it says 2 to the power 3 is greater than
5 square that means this is false next
one 3 to the power 0 is equal to 1000 to
the power 0 this is absolutely true
that's because anything to the power 0
is equal to 1 so both of these equal to
1 question number 4 expressed as a
product of prime factors only in
exponential form so
in here also whenever you have to
express as product of prime factors the
first thing that you need to do is fly
in factorization so when you do prime
factorization of 729 you see that it is
totally divisible by 3 again 243 is also
divisible by 3 so this is 27 then 3 9 27
3 3 9
therefore 729 can be written as 3 into 3
into 3 into 3 into 3 into 3 so this can
be written as 3 to the power 6 because 3
is getting multiplied 6 times in a
similar way we will do it for 64 so this
is 2 3 is a 6 to 2 so 4 to 16 or 32 2 8
16 2 4 8 2 2 so 4 so 64 is equal to 2
into 2 into 2 into 2 into 2 so again 2
is getting multiplied for 6 times so
this is equal to 2 to the power 6
therefore when you look at the final
product which is 729 into 64 this is
equal to 3 to the power 6 into 2 to the
power 6 so we have successfully
expressed this as product of prime
factors in exponential form so here 2 &
3 are the prime factors question number
5 simplifying 25 into v square into T to
the power 8 divided by 10 cube into 10
to the 8th e to the power 4 so here you
know wherever we have to simplify things
related to exponents our target is
always to convert them either into same
bases with different exponents or
different bases with same exponents so
that is what we target at so in this
case we cannot do anything with the
exponents but we can play around with
the bases for example we can write 25 as
5 into 5 so what happens you get same
base in all of these right similarly in
the denominator you can
right 10 as 2 into 5 so this becomes 2
into 5 to the power 3 into T to the
power 4 so you have a lot of numbers
where the base is fine so now let's see
so now in the numerator you consider the
three of these so here it is 1 here also
it is 1 so 5 to the power 1 plus 1 plus
2 into T to the power 8 divided by so 2
into 5 to the power 3 so what does that
mean so that can be written as 2 to the
power 3 into 5 to the power 3 into T to
the power 4 so this is 5 to the power 4
into T to the power 8 divided by 2 to
the power 3 what would be the value 2 to
the 4 4 to 8 so this would be 8 into 5
to the power 3 into T to the power 4 now
here you see this descendants they have
the same DS so it becomes 5 to the power
4 minus 3 because this is division
similarly T to the power 8 minus 4
because both again these two are
division and this divided by 8 so this
would be 5 to the power 1 into T to the
power 4 divided by 8 so this can be
written as 5 by 8 T to the power 4 so
this would be the answer so you see this
is the technique of simplifying
exponents so whenever you have exponents
all this try and target at making the
bases equal so if you have same bases
then you can apply the laws of exponents
and the entire problem gets very much
simplified now if you had not used the
law of exponents in that case you would
have actually been doing 5 into 5 25 25
into 25 6 25 so you would have been
doing those calculations which was
absolutely not needed thank you please
visit exam fee or come for free quality
education you can learn with a simple
four-step learning process wherein you
can watch video lessons you can ask your
questions you can refer notes and you
can take a free
online test we have content for class
six to twelve on physics chemistry
mathematics and biology along with
practical videos so please subscribe to
our channel for daily updates thank you
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Nov 24, 2024 Last updated |
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