If the expression is in exponential form, write it in radical form and evaluate if possible. If it is in radical form, write it in exponential form. Assume all variables represent posi-tive real numbers. -12x^1/2

Verified step by step guidance

1. Identify the given expression: \(-12x^{1/2}\).
2. Recognize that the expression is in exponential form, where the exponent \(1/2\) indicates a square root.
3. Convert the expression from exponential form to radical form: \(-12\sqrt{x}\).
4. Understand that \(x^{1/2}\) is equivalent to \(\sqrt{x}\), which is the square root of \(x\).
5. The expression \(-12\sqrt{x}\) is now in radical form, representing the same value as the original exponential expression.

Key Concepts

Exponential Form

Exponential form represents numbers using a base raised to a power, such as a^b, where 'a' is the base and 'b' is the exponent. This notation is useful for expressing large numbers compactly and for performing operations like multiplication and division more easily. In the context of the question, the expression -12x^(1/2) is in exponential form, indicating that x is raised to the power of 1/2.

Radical Form

Radical form expresses numbers using roots, such as √a, which represents the square root of 'a'. The relationship between exponential and radical forms is defined by the equation a^(1/n) = √[n]{a}, where 'n' is the degree of the root. In the given expression, converting from exponential to radical form involves rewriting x^(1/2) as √x, allowing for different ways to interpret and evaluate the expression.

Evaluation of Expressions

Evaluating an expression involves substituting values for variables and simplifying the result. In this case, since the variables represent positive real numbers, one can substitute a specific value for 'x' to compute the numerical result of the expression. Understanding how to evaluate both exponential and radical forms is crucial for solving problems and interpreting mathematical expressions accurately.