These students were asked to simplify: \( \frac{2 \cdot 3^{-4}}{5^{-2}} \) Adam wrote: \( \frac{2 \cdot 5^{2}}{3^{4}} \) Nick Wrote: \( \frac{5^{2}}{2 \cdot 3^{4}} \) Shane Wrote: \( \frac{2 \cdot 3^{4}}{5^{2}} \) (1 point) Shane is correct because all that needs to be done is to make the negative exponents positive. Adam is correct because the negative exponent moves the base to the other side of the fraction bar and makes the exponent positive. Nick is oorrect because the negative exponent in the numerator moves the whole numerator into the denominator and makes the exponent positive. None of these are correct because the students did not add the exponents in the numerator and then subtract exponents since there is division.

When dealing with negative exponents, it's crucial to remember that moving the base to the opposite side of the fraction changes the sign of the exponent from negative to positive. This means that Adam is on the right track as he effectively moved \(5^{-2}\) to the numerator as \(5^2\), and correctly converted \(3^{-4}\) to the denominator as \(3^4\). However, when simplifying fractions with exponents, it's also important to directly apply the laws of exponents. Instead of just moving bases, you should focus on calculations involving the exponents. For example, rather than simply flipping terms, it can be easier to think about the implications of the operation and combine exponents where necessary. This is a pretty common pitfall!