Changing Radicals to Exponents:

This chapter has covered solving radicals and then converting them into exponential form. It is much simpler to convert radicals to exponential form and then perform the indicated operation.

The expression ³√4 can be written with a fractional exponent as 4^1/3.  Note that this meets the condition (4 ^1/3)³ = 4 that is, the cube root of 4 cubed equals 4.  This can be expressed in the following algebraic form:

a ^I/n = ⁿ√a

The above definition is expressed in more common terms as follows:

a^m/n =(n√a)^m = ⁿ√a^m

Example:

Express the subsequent in exponential form.

³√27² = 27^2/3

√2 = 2^1/2

Example:

Solve the subsequent by first converting to exponential form.

√27. ³√27 = 27 ^½ . 27 ^1/3 = 27^5/6

but 27 = 3³

substituting:  27^5/6  = (3³)^5/6  = 3^5/2