what is 3 to the power of negative 2 divided by 3 to the power of negative 2

Question

mcq, choose one of the below answers:

a. 3 

b. 1/3 

c. 27 

d. 243

Answer 1

3^-2/3^-2=1 because numerator and denominator are the same!

Since 1 is none of the listed answer options, I would have to guess what they represent.

(a) Example: 3=3^-2/3^-3=3³/3²=3^3-2. To get the answer 3 from 3^-x/3^-y, where x and y represent positive numbers, then y-x=1, in other words the difference between the exponents must be 1, and the more negative of these must be in the denominator.

(b) ⅓. This is the inverse of (a). In this case the more negative of the exponents must be in the numerator.

(c) 27=3³ or 27=1/3^-3. Examples: 3/3^-2=3¹⁺²=3³=27; 3^-2/3^-5=3^5-2=3³=27.

(d) 243=3⁵. Examples: 3^-2/3^-7=3^7-2=3⁵=243; 3²/3^-3=3³⁺²=3⁵=243; 3³/3^-2=3³⁺²=3⁵=243.

Now check what the question should have been and then work out for yourself which answer option applies.