Answer:
a = 5 and a = -5
Step-by-step explanation:
Multiply both sides by 4: This gets rid of the denominator and isolates the term with a on the left side.
a^3 = 125 * 4
Take the cube root of both sides: Since we have a cube (a raised to the power of 3) on the left side, taking the cube root of both sides "undoes" the cube operation and isolates a.
Important Note: When taking the cube root, there might be positive and negative solutions, because cubing either a positive or negative number results in a positive number.
a = cube root(125 * 4)
Evaluate the cube root: a = 5 (because 5 cubed, or 5 x 5 x 5, equals 125)
*herefore, the solution for the equation is a = 5.
However, it's important to consider that some equations might have more than one solution due to the properties of radicals (cube root in this case). In this specific equation, a = -5 would also be a solution because (-5) cubed is -125, and dividing by 4 gives 125.
So, the complete set of solutions for the equation a^3 / 4 = 125 are a = 5 and a = -5.