 Hi and welcome to the session. I am Priyanka and I am going to help you with the following question which says simplify. These are the four parts of the question which we need to simplify and we will be doing it one by one. The first part is to simplify 2 raised to the power 2 by 3 multiplied by 2 raised to the power 1 by 5. Now after seeing the question one of the properties of the base and exponent clicks in our mind that when the base is like a to the power p when gets multiplied to a to the power q we can write it as a to the power p plus q that means we can have a common base and we can add the exponent. Now here we have a common base that is 2 and p a is 2, p is 2 by 3 and q is 1 by 5. So we can just substitute the values in this identity and carry on with our solution. It says that 2 raised to the power 2 by 3 plus 1 by 5. Now this is a fraction which has been made over here and we need to simplify this fraction. We will take 15 as our LCM we have 10 plus 3. So we have 2 raised to the power 13 by 15. Since it can't be further simplified so that means 2 13 by 15 is our required answer of the first part. Proceeding on with the next part we are given 1 divided by 3 to the power 3 bracket. The exponent is 7. Now 1 by a to the power n can be written as a to the power minus n. So we can write 1 by 3 raised to the power 3 as 3 raised to the power minus 3 to the power 7 is already given to us and then one of the properties say a to the power n to the power m can be written as a to the power n gets multiplied by m. That means the exponents will get multiplied with each other. So using this property we can write 3 raised to the power minus 3 multiplied by 7 which will make it 3 raised to the power minus 21. So this is the answer of our second part. Proceeding on with the next part it is given 11 raised to the power 1 by 2 divided by 11 raised to the power 1 by 4. Now one of the properties of base and exponents says that a to the power n divided by a to the power m can be written as a to the power n minus m. That means the base will remain the same and the exponents will get subtracted. So on doing this we have 11 raised to the power 1 by 2 minus 1 by 4. We have subtracted the exponents and let us solve these two fractions. 4 is the LCM and we have 2 minus 1 which is equal to 11 to the power 1 by 4. So this is the answer to the third part. Proceeding on with the last and final part we have 7 to the power 1 by 2 getting multiplied by 8 to the power 1 by 2. Now here the bases are not same but the exponents are same. So we can write it as one of the properties say a to the power p gets multiplied by b to the power q. Then we can multiply the bases and then can have a common exponent as in the property we have a common exponent we can have a common exponent and the bases can get multiplied. So here we will multiply the bases and can have a same exponent. So it will be 56 raised to the power 1 by 2 and this will become the answer of the last and final part which was given to us. So I hope you enjoyed the session and will be well versed with all the kind of identities that you learnt in almost each and every part of the question. Try to do as many questions of these types which involves almost all the kind of properties of bases and exponents. Bye for now.