Write out the multiplication problem. For example, you might have √2 * √3.
Rewrite the problem with one radical sign covering the values that are to be multiplied. In this example, √2 * √3 would become √2*3.
Multiply the values under the radical sign. In this example, √2 * 3 would equal √6.
Add the exponents for the multiplication of radicals containing like bases. For example, if you have √b^3 * √b^4, your answer would be √b^7.
Convert your answer containing a radical to a fractional exponent if necessary. The number to the upper left of the radical (known as the index) would be the denominator of the exponent. If there is no number to the upper left of the radical, you have a square root and the index is 2. For example, if you have the answer √b^7, you can rewrite this as b^7/2.