 Hi and welcome to the session. I'm Priyanka and I'm going to help you with the following question. It says find the values of the expressions which are given to us. So let us proceed on with our solution of each and every part one by one. The first expression is 9 raised to the power 3 by 2. Now in this type of question we always look at the denominator of the exponent and then express our base as a square of that number since we are given 2 as the denominator of the exponent. So we can write 9 as 3 multiplied by 3 and the exponent will remain the same. Proceeding on, we can write 3 raised to the power 2, the whole raised to the power 3 by 2. Now on opening the brackets, we have 3 raised to the power 2 multiplied by 3 by 2 in which 2 will get cancelled out and we left with 3 raised to the power 3 which will be 3 multiplying by 3 3 times and which gives the answer of it their product as 27. So the answer to the first part is 27, right? Proceeding on with the second part. Now here we are given 32 raised to the power 2 by 5. Now we need to express 32 as the fifth power of a number because 5 is in the denominator of the exponent. So we can write 32 as 2 multiplied by 2 multiplied by 2 5 times and this can be reduced to 2 raised to the power 5, the whole raised to the power 2 by 5, right? Proceeding on 2 raised to the power 5 multiplied by 2 by 5 in which they both will get cancelled out and we left with 2 raised to the power 2 which gives us an answer that is equal to 4. So 4 is the answer to the second part. Proceeding on further to the third part, the third expression is 16 raised to the power 3 by 4. Now you can tell me we need to express 16 as what power, right? We need to express it as a fourth part of a number. So that will be 2 into 2 into 2 into 2, right? So you are getting the point, good. Then it will be written as 2 raised to the power 4 3 by 4 and then both the exponents will get multiplied with each other and will get cancelled out. So we have 2 raised to the power 3 whose expansion will be giving us an answer of 8. So the answer to the third part is 8. Proceeding on with the last and final part, here also we need to convert 125. Now here we have a minus sign in our exponent. So firstly we will reduce it at the third power of a number that we know is 5 and then I will tell you what you will do with this minus sign. Proceeding on as we did in the above parts. Now 3 will get cancelled out. Now we are left with 5 raised to the power minus 1. Now if we have any rational number having an exponent of minus n where a and n both the base and the exponent are rational numbers. We can write it as 1 divided by a to the power n, right? So now here our a is 5 and n is 1. So we can write it as 1 by 5 raised to the power 1 which will give us the answer as 1 by 5 itself. So the answer to the last and final part is 1 by 5. So this completes the question which was given to us. I hope you enjoyed the session and remember the identity that is taught to you just now. Bye for now.