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from PIL import Image

# Open the image file to check its contents
img_path = '/mnt/data/1725505058025j631go1a.jpg'
image = Image.open(img_path)
image.show()

Simplify the following radicals:
1. (∛(27x^5y^9))/(∛(125x^7y^3))
2. √(64m^3n^6)
3. √(20u^5n^6v^7)
4. √((48t^15y^19)/(205t^28)) * 2√((16t^8)/(y^9b^12))
5. (∛(81m^3n^6p^12))/(√(270m^7n^3)) - 4m^3n^4

This lesson demonstrates how to simplify complex radical expressions involving cube roots and square roots of polynomials, such as √(64m^3n^6) and ∛(81m^3n^6p^12). Detailed steps include applying the properties of exponents and radicals, suitable for high school students in Grades 10-12.

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