How to multiply radicals with different indices?

It is easy to multiply two radical expressions of the same index. However, if you want to multiply two radical expressions with different indices, you need to follow a different procedure. If you want to multiply two radical expressions whose indices have the same sign, you just need to take the product of the radical expressions and simplify it. But if you want to multiply two radical expressions whose indices have opposite signs, you need to take the reciprocal of the smallest radical expression, take its square root, and multiply the

How to use rational exponents with radicals?

You can use a radical where the exponent is a fraction (rational exponent). For example, use the square root symbol for the radical of a square, and the radical of a fraction. To multiply two radicals, just use one exponent on each term. For example, is equivalent to In these problems, the radical symbol is used instead of the square root symbol. You will find this on a calculator, too.

How to factor radicals with different indices?

If you are given two multiples of the same radical with different indices, factor them each using the rules for indexing. If the second radical is in the denominator, then take the reciprocal of the denominator. If the second radical is in the numerator, divide the numerator by the denominator.

How to multiply complex radicals?

If you have two complex radicals with different indices, you can simplify the multiplication by using the conjugate. Remember, the product of the complex conjugate of one radical and the original radical equals -1. This means, if you simplify your two radical expressions to the complex conjugate of one, you’ll get -1 and you won’t have to worry about the opposite radical signs.

How to solve radicals with positive and negative exponents?

A radical with a positive exponent can be written using the root function. A radical with a negative exponent can be written using the reciprocal of the function. For example: If you want to solve for x, use the square root function because the exponent is a positive 2. If you want to solve for x, use the reciprocal of the square root function because the exponent is a negative -2.