In this video, let's learn about having a fraction of a rational number in the numerator so we have
all to the power one by two over here.
Now, this is equivalent to writing.
The square root of forty nine, I remember when you have a radical sign like this over here and you
don't write anything over here, it's understood that you take to over here to hope for an end to the
power.
One by two is the same as the square root of 49.
That's an interesting thing.
Now we know that seven and seven is equal to forty nine, therefore the square root of forty nine is
equal to seven.
You can note that the square root is the inverse operation of raising the number by the power to make.
You have square root and you have breaking the power to these two are inverse operations.
Now if you have thirty two to the power one by five, what do you mean with that.
Oh I can write 32 as to India, to India, to India, to India to that's five to and you raise it to
the power one by five.
So raising it to the power one by five means.
If you have five similar factors that is from a group of five you take one.
So this simplifies to two.
This can also be written as 32, taking the fifth root of 32.
So this expression and this expression means one and the same thing.
Now let's try to find out 32 to the power to buy five.
I can write this as 32 to the power one by five, to the power to write because it's the power.
Ehman can be written as to the power, to the power.
And based on the rules that we've learned now today due to the power, one by five is equal to two.
So that's two to the power two.
Which gives you the answer for let's practice a few more questions.
Say you want to simplify four to the power, five by two.
I can do this or to the power one by two, to the power five or to the power one by two is nothing but
the square root of four, which is two.
This simplifies to two to the power of five and two to the power.
Five is nothing but thirty two.
All right.
Now, you could also have done it in the opposite manner, like you would have taken it as far to the
power five to the power one by two.
In either way it simplifies to four to the power by two.
Right now, let me expand this.
This is four into four into four into four into four.
You have five fours over here and then you have your power, one by two over here.
Now, when you raise a number to the power, one by two from every two, you take one.
Right.
So you have to force over here.
You take one to take one four from these two wars.
And or can we return us to India to go from this, to take one, two.
Right.
So therefore, this is equal to for India, for India to or India for 16 16.
India two is equal to thirty to.
All right, now you can see that aid to the power embassy in is in the route of aid to the power team,
that's what we did over.
Here.
We've taken the route first and we've taken the power later, or you can do it like this where you do
the power first.
So you have taken em over here and you take the route.
That's the route over here.
The both of these are the one and the same.
And remember and has to be not equal to zero because division by zero is not defined.
All right.