1) Different indices with the same radicand can be combined by adding the indices. 2) Different indices and radicands can be combined by keeping the radicand the same and multiplying the indices together. 3) Examples are provided to demonstrate combining square roots and cube roots with the same or different indices and radicands.

1. Different Indices

2. A. Different indices with same radicands
Example 1.
𝟑
𝟑 . 𝟑 Example 2. 𝟐𝒂 .
𝟒
𝟐𝒂
= 3
1
3 . 3
1
2
= 3
1
3 +
1
2
= 3
5
6
=
6
35 =
𝟔
𝟐𝟒𝟑
(2𝑎)
1
2 . 2𝑎
1
4
= (2a)
1
2 +
1
4
= (2𝑎)
3
4
=
4
(2𝑎)3 =
𝟒
𝟖𝐚𝟑

3. B. Different Indices and Radicands
Example 3. 𝟑 .
𝟑
𝟒 Example 4.
𝟖
𝒃 . 𝟒
𝒂
= 3
1
2 . 4
1
3
= 3
3
6 . 4
2
6
= 33 . 42
1
6
=
6
33 . 42
=
6
27 . 16 =
𝟔
𝟒𝟑𝟐
= 𝑏
1
8 . 𝑎
1
4
= 𝑏
1
8 . 𝑎
2
8
= (𝑏𝑎2)
1
8
=
8
𝑏𝑎2 =
𝟖
𝒂𝟐𝒃