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Examples: Laws of Exponents Video Lecture | Mathematics for EmSAT Achieve
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FAQs on Examples: Laws of Exponents Video Lecture - Mathematics for EmSAT Achieve
| 1. What are the basic laws of exponents? |  |
Ans. The basic laws of exponents include the product rule, power rule, quotient rule, zero exponent rule, and negative exponent rule. The product rule states that when multiplying two exponential numbers with the same base, you add the exponents. The power rule states that when raising an exponential number to another exponent, you multiply the exponents. The quotient rule states that when dividing two exponential numbers with the same base, you subtract the exponents. The zero exponent rule states that any number (except zero) raised to the power of zero is equal to 1. The negative exponent rule states that any number raised to a negative exponent is equal to the reciprocal of the number raised to the positive exponent.
| 2. How do you simplify expressions with exponents using the laws of exponents? | |
Ans. To simplify expressions with exponents, you can use the laws of exponents. First, apply the product rule by adding the exponents when multiplying exponential numbers with the same base. Next, apply the power rule by multiplying the exponents when raising an exponential number to another exponent. Then, apply the quotient rule by subtracting the exponents when dividing exponential numbers with the same base. Additionally, you can use the zero exponent rule to simplify expressions by replacing any base raised to the power of zero with 1. Lastly, you can use the negative exponent rule to simplify expressions by taking the reciprocal of the base raised to the positive exponent.
| 3. How can I solve equations involving exponents using the laws of exponents? | |
Ans. To solve equations involving exponents using the laws of exponents, you can follow these steps. First, apply the appropriate law of exponents to simplify the equation as much as possible. Then, isolate the variable by performing inverse operations, such as addition, subtraction, multiplication, or division. If there are terms with the same base and different exponents on both sides of the equation, you can equate the exponents and solve for the variable. If the equation involves fractional exponents, you can convert them to radical form and solve accordingly. Remember to always check your solutions by substituting them back into the original equation.
| 4. How do the laws of exponents apply to scientific notation? | |
Ans. The laws of exponents also apply to scientific notation. When multiplying or dividing numbers in scientific notation, you can multiply or divide the coefficients and add or subtract the exponents accordingly. For example, to multiply two numbers in scientific notation, multiply their coefficients and add their exponents. To divide two numbers in scientific notation, divide their coefficients and subtract the denominator's exponent from the numerator's exponent. Additionally, the laws of exponents can be used to simplify expressions in scientific notation by applying the product, power, quotient, zero exponent, and negative exponent rules.
| 5. Can the laws of exponents be applied to all real numbers? | |
Ans. The laws of exponents can be applied to all real numbers except for zero in some cases. For example, the zero exponent rule states that any number (except zero) raised to the power of zero is equal to 1. However, raising zero to the power of zero is undefined. Additionally, the negative exponent rule can be applied to all non-zero real numbers, as it involves taking the reciprocal of the number raised to the positive exponent. It is important to note that the laws of exponents are primarily used for positive real numbers and may not hold true for complex numbers or other mathematical domains.
Text Transcript from Video
he'll open this video on powers part 6
is brought to you by exam feel calm no
more fear from exam let's look at some
questions question number one evaluate 1
by 2 to the power minus 5 so this can be
written as 1 by 2 to the power minus 5
so this means 1 to the power minus 5
divided by 2 to the power minus 5 so 1
to the power minus 5 what would be that
that would be 1 to the power minus 5 can
be written as 1 by 1 to the power 5
similarly 2 to the power minus 5 can be
written as 2 to the power 1 by 2 to the
power 5 because this we have known till
tonight so if you have 2 to the power
minus 5 which can be written as 1 by 2
to the power 5 similarly if you have 1
to the power minus 5 this can be written
as 1 times 1 to the power 5 so in this
case this meant something I did 1 to the
power minus 5 into 1 by 2 to the power
minus 5 so 1 to the power minus 5 is
written as 1 by 1 to the power 5 that 1
by 2 to the power 9 is 5 is written and
e to the power 5 so this is equal to 2
to the power 5 divided by 1 because 1
multiply 5 times 4 20 to 1 2 to the
power 5 is 3 to the 2 into 2 into 2 into
2 into 2 that is 2 to the 4 for the 8 is
16 2 into the 32 so 32 would be now
answer question number 2 simplify and
express the result in power notation
with positive exponent this is what is
given to you - 3 to the power 4
multiplied by 5 by 3 to the power 4 so
this can be written as minus 3 can be
written as minus 1 into 3 to the power 4
into 5 to the power 4 divided by 3 to
the power 4 so this can be written as
minus
to the power 4 into 3 to the power 4
into 5 to the power 4 by 3 to the power
4 so minus 1 multiplied 4 4 times this
gives you plus 1 so good minus 1 into
minus 1 so that is minus 1 into minus 1
into minus 1 into minus 1 so this gives
you 1 similarly this gives you 1 so this
will give you 1 this is 1 3 to the power
4 into 5 to the power 4 divided by 3 to
the power 4 so these two will cancel out
to give one to you I'm x 25 to the power
4 then on the sleep finding the
value of find the value of 1 by 2 to the
power minus 2 plus 1 by 3 to the power
minus 2 plus 1 by 4 to the power minus 2
so let's see how do we go about this in
this case you might see that okay the
bristles are the same this is our
difference that exponents are the same
but do we have any such law of exponent
which covers the addition of such
exponential apples not really better to
move with in this fashion so 1 by 2 to
the power minus 2 is something like this
similarly 1 by 3 to the power minus 2
plus 1 by 4 to the power minus 2 so this
can be written as 2 to the power 2 plus
3 to the power 2 plus 4 to the power 2
so 2 to the power 2 is 4 that is 2 into
2 3 into 3 is 9 4 into 4 is 16 so this
is 4 plus 25 which is equal to 29
question number 4 evaluate 8 to the
power minus 1 into 5 to the power 3
divided by 2 to the power minus 4 let's
see how to be handled is 8 to the power
minus 1 can be written as 1 by 8 to the
power 1 which is 1 by 8 5 to the power 3
and the left as it is 1 by 2 to the
power minus 4 can be written as 2 to the
power plus 4 right ok now this can be
written as 1
now what is 8 8 is 2 to the power 3 2
into 2 into 2 is a so this into 5 to the
power 3 into 2 to the power 4 so this
can be written as 5 to the power 3 into
2 to the power 4 by 2 to the power 3 so
when you look at this here you have seen
these different exponents and they are
taking divided so this can be written as
the base and the exponent get subtracted
so 2 to the power 4 minus 3 so this
would be 5 to the power 3 into 2 to the
power 1 5 into 5 into 5 is 125 into 2
that is equal to 250 ready number 5 find
the value of n for which 5 to the power
n divided by 5 to the power minus 3 is
equal to 5 to the power 5 let's feed is
5 to the power M divided by 5 to the
power minus T will be equal to 5 to the
power 5 so you these are same basis
different exponents and they are getting
divided so the exponent will get
subtracted so M minus minus 3 this is
equal to 5 to the power 5 nothin on the
rest hand side right hand side the bases
are the same so for the entire value to
the same the exponent should also be
equal therefore we can say that n Mandal
minus 3 should be equal to fight that is
this exponent should be equal to this
exponent or this can be written as n
plus 3 is equal to 5 or PHA n is equal
to 5 minus 3 therefore n is equal to 2
question on the stage 25 into T to the
power minus 4 divided by 5 to the power
minus 3 into 10 into T to the power
minus 8 so how do we solve this now 25
let's eat 25 and 5 together so 1 by 5 to
the power minus 3 can be read
five to the power three perfect now and
let's see can all show it at ease and
what about P P can be written as minus
four minus minus eight that's because T
to the power minus four divided by P to
the power minus eight the same B's
different exponents they are getting
divided so the exponent will actually
get subtracted so this becomes equal to
25 can be written as 5 to the power 2
into 5 to the power 3 divided by 10 into
T to the power minus 4 plus 8 so here
again same being different exponent and
they are getting multiplied so the
exponents will get added so T to the
power 4 so this becomes 5 to the power 5
divided by 10 into T to the power 4 now
this can also be written as 5 into 5 to
the power 4 by 10 so 5 to the 10 and P
to the power 4 the final answer would be
5 to the power 4 3 to the power 4
divided by 2 thank you please visit
example.com for free quality education
you can learn with a simple four-step
learning process wearing 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 6 to 12 on physics chemistry
mathematics and biology along with
practical videos so please subscribe to
our channel for daily updates thank you
is brought to you by exam feel calm no
more fear from exam let's look at some
questions question number one evaluate 1
by 2 to the power minus 5 so this can be
written as 1 by 2 to the power minus 5
so this means 1 to the power minus 5
divided by 2 to the power minus 5 so 1
to the power minus 5 what would be that
that would be 1 to the power minus 5 can
be written as 1 by 1 to the power 5
similarly 2 to the power minus 5 can be
written as 2 to the power 1 by 2 to the
power 5 because this we have known till
tonight so if you have 2 to the power
minus 5 which can be written as 1 by 2
to the power 5 similarly if you have 1
to the power minus 5 this can be written
as 1 times 1 to the power 5 so in this
case this meant something I did 1 to the
power minus 5 into 1 by 2 to the power
minus 5 so 1 to the power minus 5 is
written as 1 by 1 to the power 5 that 1
by 2 to the power 9 is 5 is written and
e to the power 5 so this is equal to 2
to the power 5 divided by 1 because 1
multiply 5 times 4 20 to 1 2 to the
power 5 is 3 to the 2 into 2 into 2 into
2 into 2 that is 2 to the 4 for the 8 is
16 2 into the 32 so 32 would be now
answer question number 2 simplify and
express the result in power notation
with positive exponent this is what is
given to you - 3 to the power 4
multiplied by 5 by 3 to the power 4 so
this can be written as minus 3 can be
written as minus 1 into 3 to the power 4
into 5 to the power 4 divided by 3 to
the power 4 so this can be written as
minus
to the power 4 into 3 to the power 4
into 5 to the power 4 by 3 to the power
4 so minus 1 multiplied 4 4 times this
gives you plus 1 so good minus 1 into
minus 1 so that is minus 1 into minus 1
into minus 1 into minus 1 so this gives
you 1 similarly this gives you 1 so this
will give you 1 this is 1 3 to the power
4 into 5 to the power 4 divided by 3 to
the power 4 so these two will cancel out
to give one to you I'm x 25 to the power
4 then on the sleep finding the
value of find the value of 1 by 2 to the
power minus 2 plus 1 by 3 to the power
minus 2 plus 1 by 4 to the power minus 2
so let's see how do we go about this in
this case you might see that okay the
bristles are the same this is our
difference that exponents are the same
but do we have any such law of exponent
which covers the addition of such
exponential apples not really better to
move with in this fashion so 1 by 2 to
the power minus 2 is something like this
similarly 1 by 3 to the power minus 2
plus 1 by 4 to the power minus 2 so this
can be written as 2 to the power 2 plus
3 to the power 2 plus 4 to the power 2
so 2 to the power 2 is 4 that is 2 into
2 3 into 3 is 9 4 into 4 is 16 so this
is 4 plus 25 which is equal to 29
question number 4 evaluate 8 to the
power minus 1 into 5 to the power 3
divided by 2 to the power minus 4 let's
see how to be handled is 8 to the power
minus 1 can be written as 1 by 8 to the
power 1 which is 1 by 8 5 to the power 3
and the left as it is 1 by 2 to the
power minus 4 can be written as 2 to the
power plus 4 right ok now this can be
written as 1
now what is 8 8 is 2 to the power 3 2
into 2 into 2 is a so this into 5 to the
power 3 into 2 to the power 4 so this
can be written as 5 to the power 3 into
2 to the power 4 by 2 to the power 3 so
when you look at this here you have seen
these different exponents and they are
taking divided so this can be written as
the base and the exponent get subtracted
so 2 to the power 4 minus 3 so this
would be 5 to the power 3 into 2 to the
power 1 5 into 5 into 5 is 125 into 2
that is equal to 250 ready number 5 find
the value of n for which 5 to the power
n divided by 5 to the power minus 3 is
equal to 5 to the power 5 let's feed is
5 to the power M divided by 5 to the
power minus T will be equal to 5 to the
power 5 so you these are same basis
different exponents and they are getting
divided so the exponent will get
subtracted so M minus minus 3 this is
equal to 5 to the power 5 nothin on the
rest hand side right hand side the bases
are the same so for the entire value to
the same the exponent should also be
equal therefore we can say that n Mandal
minus 3 should be equal to fight that is
this exponent should be equal to this
exponent or this can be written as n
plus 3 is equal to 5 or PHA n is equal
to 5 minus 3 therefore n is equal to 2
question on the stage 25 into T to the
power minus 4 divided by 5 to the power
minus 3 into 10 into T to the power
minus 8 so how do we solve this now 25
let's eat 25 and 5 together so 1 by 5 to
the power minus 3 can be read
five to the power three perfect now and
let's see can all show it at ease and
what about P P can be written as minus
four minus minus eight that's because T
to the power minus four divided by P to
the power minus eight the same B's
different exponents they are getting
divided so the exponent will actually
get subtracted so this becomes equal to
25 can be written as 5 to the power 2
into 5 to the power 3 divided by 10 into
T to the power minus 4 plus 8 so here
again same being different exponent and
they are getting multiplied so the
exponents will get added so T to the
power 4 so this becomes 5 to the power 5
divided by 10 into T to the power 4 now
this can also be written as 5 into 5 to
the power 4 by 10 so 5 to the 10 and P
to the power 4 the final answer would be
5 to the power 4 3 to the power 4
divided by 2 thank you please visit
example.com for free quality education
you can learn with a simple four-step
learning process wearing 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 6 to 12 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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Dec 24, 2024 Last updated |
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