\large \frac{2\cdot3^{-4}}{5^{-2}}
Adam wrote: \large \frac{2\cdot5^2}{3^4}

Nick wrote: \large \frac{5^2}{2\cdot3^4}

Shane wrote: \large \frac{2\cdot3^4}{5^{^2}}

Who is correct and why?

a
Adam is correct because the negative exponent moves the base to the other side of the fraction bar and makes the exponent positive.
b
None of these are correct because the students did not add the exponents in the numerator and then subtract exponents since there is division.
c
Nick is correct because the negative exponent in the numerator moves the whole numerator into the denominator and makes the exponent positive.
d
Shane is correct because all that needs to be done is to make the negative exponents positive.