
Please check this work
Hello.
well, my professor provided us with an exam review with its solution, but I don't understand an exercise, could you please go to this link http://www.accd.edu/sac/math/faculty.../PdfT2BRev.pdf and take a look on exercise number 18, I do not understand from where did my professor get that 3/2 exponent, is that right? shouldn't it a 1/3 exponent?
another thing, I'm having this exam on logs in two days, could you please give me any tips to do well in this exam, also if you know any good site concerned this topic.
Thank you.

No your instructor is correct: $\displaystyle \sqrt {a^3 } = a^{\frac{3}{2}} $.

thanks
Thank you plato for your help, but why 3/2? I thought we were looking for the opposite of cube root which is 1/3
also, could you please go to that link again, and tell me why did my professor solve exercises 14 and 15 without including logs, why?
I think exercises 13 and 14 are very similar, however my professor solve exercise number 13 using logs but in exercise 14 did not use logs.
thanks.

Remember that $\displaystyle \frac{1}{9} = 3^{2}$
Your professor noticed that and made them both have the same base. Once they have the same base you can drop the base and just solve for x.

Frankly I do not understand your confusion.
You simply need to review the use of fractional exponents.
The review you were given is correct.
Your understanding of fractional exponents is incorrect.

Thank you plato, but I think you are referring to exercise number 14, I don't have problems understanding this exercise, I'm having trouble understanding exercise number 18.
and please tell me why did my professor didn't include the word "log" when solving exercises number 14 and 15.
Thank you.