Simplify: (3^(2)*3^(-1))/(5^(-2)*2^(0))

Question

adam wrote: (3^(-2)*5^(2))/(2)
nick wrote: 3*5^(2)
shane wrote: (3^(-3))/(5^(2))
who was correct and why?
a. shane is correct because all that needs to be done is to make the negative exponents positive
b. adam is correct because the negative exponent combines with the base and the denominator moves to the numerator
c. nick is correct because the negative exponent in the numerator can combine with the like base and the denominator negative exponent goes to the numerator
d. none of these are correct because the students did not add the exponents in the numerator and then subtract exponents since there is division

Answer 1

b. adam is correct because when dividing with exponents, you subtract the exponents. Additionally, the negative exponents combine with the base to move from the numerator to the denominator (or vice versa).