The value of sqrt[4](625)^3 is:

The correct answer is Option (3) → 125

The fourth root of a cube is the power \(\frac{3}{4}\), and 625 is a fourth power (\(625=5^4\)).

• Writing 625 as \(5^4\): \(\sqrt[4]{(625)^3}=(5^4)^{\frac{3}{4}}\)

• The powers multiply, \(4\times\frac{3}{4}=3\), so the value is \(5^{3}=125\)