Here's how to simplify 4/(1 - 3^(1/3) + 9^(1/3)):
Recognize the Pattern: This expression involves the cube roots of 3 and 9. We know that 3^(1/3) = 3 and 9^(1/3) = 2.
Substitute the Values: Rewrite the expression with these values:
4 / (1 - 3 + 2)
Simplify the Denominator: Combine the terms in the denominator:
4 / (-1)
Division: Divide the numerator by the denominator:
4 / -1 = -4
Therefore, the simplified form of the expression is -4.