Final answer:
To solve the equation, multiply both sides by 64, add 25, divide by 64, and take the cube root of (25/64) raised to the power of 3/2.
Step-by-step explanation:
To solve the equation y^((2)/(3))-25/(64)=0, we can start by getting rid of the fraction by multiplying both sides of the equation by 64. This gives us: 64*y^((2)/(3))-25 = 0. Next, we can add 25 to both sides to isolate the term with the variable: 64*y^((2)/(3)) = 25. Finally, we can solve for y by dividing both sides by 64 and then raising both sides to the power of 3/2. This gives us: y = (25/64)^((3)/(2)). The answer is the cube root of (25/64) raised to the power of 3.