Review of Introductory Mathematics RADICALS Dissimilar Radicals Often, dissimilar radicals may be combined after they are simplified. Example: 4 81x² x 6 64x³ 3  x x 2  x (3 1 2) x 2  x Changing Radicals to Exponents This chapter has covered solving radicals and then converting them into exponential form. It is much easier to convert radicals to exponential form and then perform the indicated operation. The expression can be written with a fractional exponent as 4^1/3.   Note that this meets the 3 4 condition , that  is, the cube root of 4 cubed equals 4.   This can be expressed in the 4 1 3 3 4 following algebraic form: a^1/n n a The above definition is expressed in more general terms as follows: a^m/n n a m n a^m Example 1: Express the following in exponential form. 3 27² 27^2/3 2 2^1/2 Example 2: Solve the following by first converting to exponential form. 27 3 27 27^1/2 27^1/3 27^5/6 but 27 = 3³ substituting:   27^5/6 = (3³)^5/6 = 3^5/2 Rev. 0 Page 77 MA-01