Week Two Math 10

What I have learned in Math 10 this week

( $\frac{-5k^3\cdot k^2}{k^2} )^2\cdot ( \frac{(-k)^5\cdot k^2}{5k^2}$ )

I had turned it into $\frac{25k^10}{k^2}$ which is correct but on the right side it’s $\frac{-k^7}{5k^2}$ . I thought it would’ve turned into $25k^8\cdot-5k^5$ equaling $-k^13$ .

Instead Ms Burton taught me since the 5k was on the bottom it would have been $-0.2^5$ . There for it has to be $\frac{25}{1}$ $\frac{1}{-5k}$ left as a fraction.

My answer of $-K^13$ was not correct contradicting the book oddly leaving it according to Ms. Burton to be a fraction.

I have also learned quite a bit about negatives but still learning as I am unfamiliar to negative exponents. I know for example to make a $4x^-6$ positive is to turn it into a fraction. IE $\frac{4}{x^6}$

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