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 \sqrt[3]{-1000 x^{6} y^{12}  }

Since the index is three, find for their cube root.

     ·The cube root of -1000 is -10.

     ·The cube root of x⁶ is.
                 *How did we get x² ? Just simply divide the exponent of the variable inside by the index so 6 divided by 3 is 2, then just copy the variable so we got x².

     ·The cube root of y¹² is y⁴.

Combine them all, so the answer is -10x²y⁴.