Radical and Exponent Relationship
radicalparats
We know that if we square the square root of 3, the result will be simply the radicand 3.
Squaring the square root of the number 3 will leave just the number 3.

"Matching" radicals and exponents are inverse operations.


repic3
repic1

The solution to each radical, when raised to the radical's index, gives the radicand.
Symbolically, we have:  

Applying this relationship, as shown below, we can arrive at the conclusion
that a radical of index "n" raised to a power of "n", will return the radicand "a".

Radical functions and power functions can be inverses of one another.

 

Radicals and fractional exponents:
repic6

The denominator of the fractional exponent will be the index of the radical.


If n is a positive integer that is greater than 1 and a is a real number, then
infodef

When a is nonnegative, n can be any index.
When a is negative, n must be odd.
For work in this unit, you may assume, unless otherwise directed, that all variables in radicands ("a")
represent non-negative real numbers and that the radicand is non-negative.


When dealing with radicals, it may be advantageous to rewrite the radical using a fractional exponent. The power rules associated with exponents often make the radical computations or simplifications easier.
Note: We can also say: infon

See more about fractional exponents at Fractional (Rational) Exponents.
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