I have a question on this problem on Chapter 14 Number 10 in the 5lb book(pg.465) on the topic of Exponents and Roots.

I was able to get the correct equation from the question of (x^2)/the cubed root of x=9x

however I solved it wrong. My question is can you also solve it by breaking down the first half of the equation into x^2 * x^-3 then combining the exponents to x^-1.

Then making x^-1 = 9x?

Thats how I went about solving it. (the last picture)

\frac{1}{\sqrt[3]{x}} \neq x^{-3}

That’s your mistake.

ok thank you I see my mistake now

would the correct conversion be: (x)^-1/3 ?

Correct.