Simplifying rational exponent expressions: mixed exponents and radicals

so I have an interesting equation here it says V to the negative 6/5 power times the fifth root of V is equal to V to the K power for V being greater than equal to zero and what I want to do is try to figure out what K needs to be so what is what is K going to be equal to so pause the video and see if you can figure out K and I'll give you a hint you just have to leverage some of your exponent properties all right let's work this out together so the first thing I'd want to do is is be a little bit consistent in and how I write my exponents so here I've written it as negative 6/5 power and here I've written it is a fifth root but we know that the fifth root of something we know that the fifth root the fifth root of V that's the same way that's the same thing as saying V to the 1/5 power and the reason I want to say that is because then I'm multiplying two different powers of the same base two different powers of V and so we can use our exponent properties there so this is going to be the same thing as V to the negative 6/5 times instead of saying the fifth root of V I can say times V to the 1/5 power is going to be equal to V to the K it's going to be equal to V to the K power now if I if I'm multiplying V to some power times V to some other power we know what the exponent properties would tell us and I could remind us I'll do it over here if I have X to the a times X to the B that's going to be X to the a plus B power so here I have the same base V so this is going to be V to the and I can just add the exponents V to the negative 6/5 power plus 1/5 power or neither V to the negative 6/5 plus 1/5 power is going to be equal to V to the K is equal to V to the K I think you might see where this is all going now so this is going to be equal to V so negative 6/5 plus one-fifth is going to be negative 5/5 or negative one so all of this is going to be equal to negative one and that's going to be equal to V to the K so K must be equal to negative one and we're done K is equal to negative one