If \(\sqrt[3]{x}=2y\), then the value of \(\frac{y^3}{x}\) is _____
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{1}{8}\)
Cubing both sides removes the cube root and gives \(x\) in terms of \(y\).
\(\sqrt[3]{x}=2y\), so \(x=(2y)^3=8y^3\)
Putting \(x=8y^3\) in the expression, \(y^3\) cancels: \(\displaystyle \frac{y^3}{8y^3}=\frac{1}{8}\)