Final answer:
The equation that is part of the same fact family as 5x⁴ = 20 is x⁴ = 4, obtained by dividing both sides of the original equation by 5. Alternatively, the equation 20 / x⁴ = 5 is also a member of the same fact family, derived from the inverse division operation.
Step-by-step explanation:
The question asks which equation is part of the same fact family as the equation 5x⁴ = 20. A fact family in mathematics is a set of related mathematical facts or equations that are derived from the same set of numbers and operations. In this case, the given equation involves multiplication. When we look for other members of this fact family, we are looking for equations that can be formed using the inverse operations of multiplication, which is division, as well as the numbers involved in the equation, which are 5, 4 and the result 20.
From the equation 5x⁴ = 20, we can derive the equation x⁴ = 20 / 5 by dividing both sides of the equation by 5. The result of this division gives us x⁴ = 4, making this equation a member of the same fact family. Similarly, we can also derive the inverse division equation 20 / x⁴ = 5 by considering the original equation as a product of x⁴ and 5, meaning that 20 divided by one of those numbers gives us the other number.