Final answer:
The expression a^1/2 is equivalent to the square root of a. This reflects the principle that a number raised to the power of 1/2 corresponds to the square root of that number, which is an inverse operation of squaring.
Step-by-step explanation:
To write the expression a^1/2 as a radical expression, we can follow the principles of exponentiation and roots outlined in mathematical notation. A power of 1/2 is equivalent to the square root, as seen in equations such as x^2 = √x. This can also be interpreted as the inverse operation of squaring a number. To take any number to the power of 1/2 means to find the number that, when squared, would equal the original number.
The term a^1/2 is therefore equivalent to the square root of a, which is denoted as √(a). This operation is fundamental in algebra and appears in many different contexts, from solving quadratic equations to applications in physics and engineering. Remember that the square root of a number yields a value which, when multiplied by itself, gives back the original number.
Furthermore, understanding the relationship between exponents and roots is essential for working with scientific notation, simplifying algebraic expressions, and performing operations with complex numbers.