Final answer:
The expression with a rational exponent ((4 2/5)^¹⁄₄) can be rewritten as a radical expression as (c) (√[4]4 × √[4]2/5), which is the fourth root of 4 multiplied by the fourth root of 2/5.
Step-by-step explanation:
The student asked to rewrite the expression with a rational exponent as a radical expression: ((4 2/5)^¹⁄₄). Remember that when we have a rational exponent, the numerator of the exponent indicates the power, and the denominator indicates the root. So, the given expression ((4 2/5)^¹⁄₄) means we need to take the fourth root of 4 2/5.
Writing this in radical form, we have √[4]4 2/5, which can be rewritten as the product of the fourth root of 4 and the fourth root of 2/5, giving us option (c) (√[4]4 × √[4]2/5). This expression represents taking the fourth root of both 4 and the fractional part, 2/5 separately, then multiplying the results together