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The problem

I do not understand how the exponents are simplified to

$\frac pq-1$

in the expression in the image

AlgTop1854
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user1230116
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    Welcome to MSE. Take a look at some questions and answers and you will find that (even for questions on basic algebra or pre-calculus) that they are better received when the poster gives some explanation of what they tried and where they got stuck. For example, do you know basic rules of exponents but did not see how to apply them here, or have you not learned them at all yet? – AlgTop1854 Oct 04 '23 at 18:46
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    Additionally it is much better to write your question in math symbols than insert a picture. MSE supports an inline version of LaTex for this (called MathJax) and you can find tutorials for it in the help. I made a small edit to your question so you see an example. – AlgTop1854 Oct 04 '23 at 18:48

1 Answers1

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Well in the interest of closing this out:

The basic rules of exponents state that

$x^ax^b = x^{a+b}$ and
$\frac{x^a}{x^b} =x^{a-b}$

We start by requiring that $a$ and $b$ be integers but later on realize this works for rational numbers such as $p/q$ in your example and even all real numbers.

In your example, we can ignore $p/q$ on the left in each expression and apply the second rule above:

$\frac{x^p}{x^{p-p/q}} = x^{p-1-(p-p/q)} = x^{p/q-1}$

As an aside, the RHS of the original sure looks like a derivative but I can't see where the LHS came from.

AlgTop1854
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