Multiplying Radicals with Different Indices

What is the basic rule for multiplying radicals directly?

• Radicals can be multiplied directly if their indices are the same.

• Radicals can be multiplied directly if their radicands are the same.

• Radicals can be multiplied directly if their exponents are the same.

• Radicals can be multiplied directly if their bases are the same.

In the shortcut method, what is the first step when multiplying radicals with the same radicand but different indices?

• Simplify the radicands first.

• Create a single radical and multiply their indices.

• Convert the radicals to rational exponents.

• Add the indices together.

When using the shortcut method, how do you determine the new index for the radicals?

• By adding the indices of the radicals.

• By dividing the larger index by the smaller index.

• By multiplying the indices of the radicals.

• By subtracting the smaller index from the larger index.

In the second example, what serves as the exponent of the first radicand?

• The product of the indices.

• The index of the first radical.

• The sum of the indices.

• The index of the second radical.

What is the final result of multiplying the radicals in the second example?

• The sixth root of 432

• The sixth root of 32

• The third root of 432

• The fourth root of 432