Final answer:
The equation 1/4x^3 = -27/4 is solved by first multiplying both sides by 4 and then taking the cube root of both sides, resulting in the solution x = -3.
Step-by-step explanation:
To solve the equation 1/4x^3 = -27/4 using inverse operations, we start by multiplying both sides of the equation by 4 to eliminate the fraction on the left side:
4 * (1/4x^3) = 4 * (-27/4)
x^3 = -27
Now we take the cube root of both sides to solve for x:
∛x^3 = ∛-27
x = -3
Thus, the solution to the equation is x = -3.