Final answer:
The question hints at solving quadratic equations and performing algebraic manipulations like factoring, completing the square, or using the quadratic formula. For equations with roots, inverse operations like raising to the power of 0.5 or 0.25 are used.
Step-by-step explanation:
It appears there's some confusion in the original question. It mentioned an expression (4a^2b^4) and it seems to relate to the topic of quadratic equations and algebraic manipulation. To address similar problems, you would typically engage in factoring, completing the square, or applying the quadratic formula as relevant to the equation at hand.
For instance, if you have a quadratic equation in the standard form at^2 + bt + c = 0, you can find its solutions by using the quadratic formula. This formula is derived from the process of completing the square and it provides the roots of the quadratic equation. Remember that when you work with equations, there can be intermediate steps which require rounding off to a certain number of significant figures.
In the case of extracting roots (such as sqrt or fourth root), algebraic manipulation includes applying inverse operations, such as raising numbers to the power of 0.5 for the square root or 0.25 for the fourth root. These techniques are essential in solving equations that involve powers and inverse operations.