In the expression x to the power of p/n, what is indicated by n?

In the expression ( x^{p/n} ), the term ( n ) is specifically the denominator of the fraction. This is because the fraction is structured as ( p ) divided by ( n ), where ( p ) represents the exponent and ( n ) indicates how many times the base ( x ) is multiplied by itself. More explicitly, if ( n ) is greater than 1, ( x^{p/n} ) denotes the ( n )-th root of ( x^p ).

To clarify further, when ( n ) is used in the denominator of a fractional exponent, it informs us that we are taking a root of some sort. For example, ( x^{1/2} ) means the square root of ( x ), reflecting that the numerator indicates the power and the denominator indicates the root. The function of ( n ) is crucial for understanding how the exponentiation and rooting interact within this expression. Thus, identifying ( n ) as the denominator of the fraction correctly summarizes its role in this mathematical representation.