What does x to the power of 1/n denote?

The expression ( x^{1/n} ) represents the n-th root of ( x ). This means that it denotes a value that, when raised to the power of ( n ), yields ( x ). Mathematically, if ( y = x^{1/n} ), then raising ( y ) to the n-th power gives ( y^n = x ). This is a fundamental concept in mathematics, linking exponentiation and roots.

For example, if ( n = 2 ), then ( x^{1/2} ) is the square root of ( x ). Similarly, if ( n = 3 ), then ( x^{1/3} ) is the cube root of ( x ). This relationship between exponents and roots is a crucial part of understanding how to manipulate and interpret algebraic expressions involving powers.