I already apologize for the banality of the question but I've come across the following GRE question and wanted to ask whether this is really a well-defined exercised.
One has to compare quantities and decide whether quantity A or quantity B is greater, whether they are equal or whether the relationship cannot be determined from the information given.
Here's the full question for completeness:
$$–1 < a < 0 < |a| < b < 1$$
Quantity A: $$\biggl(\frac{a^2\sqrt{b}}{\sqrt{a}}\biggr)^2$$ Quantity B: $$\biggl(\frac{ab^5}{(\sqrt{b})^{4}}\biggr)$$
I am only curious about the denominator in quantity A, which I believe is not well defined since we are taking the square root of a negative number and $(\sqrt{a})^2 \neq \sqrt{a^2}$.
In the solution to the question in the GRE book they "use exponent rules" to simplify the expression to $\frac{a^4b}{a}$ and conclude that quantity A is greater. This seems so obviously wrong, have I missed something or is that a mistake in the question?