# Question Video: Manipulating Exponential Expressions Mathematics

If the expression (2/3)^(β2π¦) is rewritten in the form π^(π¦), what is the value of π?

02:03

### Video Transcript

If the expression two over three to the power of negative two π¦ is rewritten in the form π to the power of π¦, what is the value of π?

So first of all, letβs consider what two over three or two-thirds to the power of negative two π¦ means. Well, to do this, what weβre gonna use is some exponent rules. Well, the first rule weβre gonna use is the fact that if we have π₯ to the power of π and then this is to the power of π, then this is equal to π₯ to the power of π multiplied by π. And in fact, weβre gonna use this in reverse because what we can do is rewrite our expression two over three or two-thirds to the power of negative two π¦ as two over three to the power of negative two. And then this is all to the power of π¦.

And the reason weβve done this is because what weβre looking for is to get our expression in the form π to the power of π¦, so something to the power of π¦. Well, next, what weβre gonna do is use another one of our exponent rules. And that is, if we have π₯ over π¦ to the power of negative π, then this is equal to the reciprocal of our fraction, so π¦ over π₯ to the power of π. And what this is is an adaptation of the exponent rule, which tells us that π₯ to the power of negative π is equal to one over π₯ to the power of π.

Okay, great. So letβs apply this to our problem we have. So when we do that, what we have now is the reciprocal of two-thirds or two over three, which is three over two or three-halves, all to power of two. And then this is to the power of π¦. Well, if we get back to the question, what we were looking for is we want the expression rewritten in the form π to the power of π¦. Well, we have that because we have something to the power of π¦. So now, what we need to do is identify what the value of π is. So therefore, we can say that π is gonna be equal to three over two or three-halves all squared. Itβs also worth noting that we couldβve written this as nine over four.

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