Possible error regarding ch3 of foundation of math dril3 q.5

[daviddinan]

Hi. 7th edition of foundation of math
Ch.3, drill 3 question 5, I believe answers of 2 power of negative 2/ 3 power of zero

And answer choice , -3 power of power of 3 / -5 power of 2 , are values lesser than 1. Or am I wrong ?

[Sage Pearce-Higgins]

To be clear, we're talking about problem 25 at the end of the Drill Set of Chapter 3 (Exponents).

(A) less than zero. Any number to the power of 0 equals 1, so we can ignore the 3^0. A negative power simply means "reciprocal", so 2^(-2) = 1/(2^2) = 1/4
(B) Being careful about the reciprocals, this one equals (1/3^2) / (1/4^2). Dividing by a fraction is the same as multiplying by its reciprocal (for example dividing by 1/2 is the same as multiplying by 2/1: see more about dividing fractions on this). So I can 'flip the bottom fraction and multiply' to get (1/9) x (16/1). This is bigger than 1.
(C) The bottom of this fraction is positive, but the top is negative, so the fraction is less than 1.
(D) Again, the reciprocal makes this (3/2)^2. This is bigger than 1.
(E) This is negative, so it's less than 1.

I don't see any errors here. However, I'm not sure if I fully understood your question.