 Hi, and how are you all today? I'm Priyanka and let us proceed on to the questions solution which is given to us These are the three parts of the question which are given to us and we need to find its value So let us proceed on to the first part 64 to the power 1 by 2 Now in these type of question as you remember you did in your previous classes also You need to write 64 as a square of a number we know that 64 can be written as 8 multiplied by 8 right and then 8 is coming two times so we can write 8 to the power 2 In place of 8 multiplied by 8 Now when we open the brackets 8's exponent will get multiplied by the exponent that is outside using the property that 8 to the power m to the power n is equal to a to the power m multiplied by n Now 2 will get cancelled out with each other and we are left with 8 to the power 1 Which can be written as 8 only so 8 is the answer of our first part Proceeding on with the next part Now we are given 32 to the power 1 by 5 Similarly as we did in the above question also we need to write 32 as the fifth power of a number We can write 32 as 2 multiplied by 2 multiplied by 2 5 times Right because their product will be equal to 32 only Proceeding on we can write 2 to the power 5 as it is occurring five times and Then using the same identity Which is 8 to the power m to the power n is equal to a m multiplied by n So we can open the brackets 2 to the power 5 multiplied by 1 by 5 They both will get cancelled out and we are left with 2 to the power 1 Whose answer will be 2 itself. So this completes the second part Proceeding on with the third and final part Now we are given 125 raised to the power 1 by 3 again 125 can be written as 5 multiplied by 5 multiplied by 5 right We can write it as 5 to the power 3 the whole to the power 3 on opening the brackets 3 we'd get multiplied by 1 by 3 They both will get cancelled out and we're left with 5 to the power 1 and Hence our answer will become 5 so this completes the entire question which was given to us I hope you remembered your identity that is when a to the power m gets multiplied by n on opening the brackets the Exponents get multiplied by each other Right so knowledge of this identity will help you in solving these type of questions So I hope you enjoyed the session. Bye for now