Answer:
10x^2y^6√y
Explanation:
1. First, let's factor out any perfect squares from the expression under the square root. In this case, we can factor out 100, which is a perfect square:
√(100 * x^4 * y^13)
2. Taking the square root of 100 gives us 10:
10 * √(x^4 * y^13)
3. Now, let's simplify the expression under the square root. Remember that the square root of a product is equal to the product of the square roots:
10 * √(x^4) * √(y^13)
4. The square root of x^4 is x^2:
10 * x^2 * √(y^13)
5. Finally, let's simplify the square root of y^13. Since 13 is an odd number, we can write it as the product of a perfect square and an additional factor:
10 * x^2 * √(y^12 * y)
6. The square root of y^12 is y^6:
10 * x^2 * y^6 * √y
Therefore, the simplified expression for the square root of -100x^4y^13 is:
10x^2y^6√y