How do you multiply radicals with different indices?

One of the most common mistakes that beginning algebra students make is to forget to change the index on each radical when multiplying two radicals with different indices. When you want to solve this problem, you should use the index property to combine the two radicals.

How to multiply radicals with different indices?

If you want to find the product of two radicals with different indices, you must do something called normalization. This involves multiplying each radical by its denominator. That's why the radical signs are often represented by the number 1. So for example, is the product of and If you perform the normalization step for each radical, you will end up with

How to multiply radicals with exponent?

The easiest way to multiply radical expressions with exponent is by using the exponentiation operation. This operation is represented by the ^ symbol (caret). The exponents are placed on top of the radical symbol. You usually do not need a space between the two symbols, as they are automatically placed on top of each other. However, if you wish to add another radical or an expression that contains one, you will need to add a space between the two.

How to solve radicals with different indices?

Let's say that you are given two radical expressions with different indices (while keeping the same base). For instance, and These are the same function, but with different index notation. You can solve these expressions by multiplying them with the reciprocal of the base.

How to multiply radicals with the same indices?

When you have two radicals with the same index and you want to multiply them, you can just add their exponents together. For example, can be multiplied by with the same index by adding the exponents: The reason that multiplying works in this case is because addition and multiplication are both distributive operations. In this case, adding the exponents is equivalent to multiplying both the numerator and denominator by the exponent of the radical, which is for