Is Y^a/Y Equal to 1/Y^1-a in Mathematics?

[albert2008]

Dear People,
I'm sorry that I am putting this question here because it might be very obvious and it might insult some of your intellingence.

Question
I know that Y/Y^a equals

Y^1-a

Does this mean that

Y^a/Y equals

1/Y^1-a ,I just want to know where this is true?

Thank you so much for putting up with my questions.

Peace to all.

 

[statdad]

For both answers

$$\frac{Y}{Y^a} = Y^{1-a}$$

$$\frac{Y^a}{Y} = Y^{a-1} = \frac{1}{Y^{1-a}}$$

In general:

$$\frac{Y^m}{Y^n} = Y^{m-n} = \frac{1}{Y^{m-n}}$$

think this way: when you have a fraction in which powers of the same quantity appear in the numerator and denominator, subtract exponents in the order "top - bottom"