Multiplying Radicals | Dividing Radicals | Multiply or Divide Radicals with Different Indices

Note: In the last problem, the fourth root of the cube root of x is equal to the 12th root of x. Hence, to reduce two radical symbols to one, simply multiply the two given indices.
In multiplying or dividing radicals, the expressions should have the same indices. If the given indices are different, re-write one or both expressions to get a common index. The latter is the least common multiple of the two given indices. Once the indices are the same, we have to multiply or divide the radicands using the laws of exponents. Once the resulting radicand is simplified, we have to evaluate the radical. To get the nth root, simply divide the exponent of each number or variable by the index. If there is a remainder in dividing the exponent by the index, leave the remainder inside the radical symbol.