Evaluate each expression 16^(1/2)

Verified step by step guidance

1. Identify the expression: You need to evaluate \(16^{1/2}\).
2. Recognize that the expression \(16^{1/2}\) represents the square root of 16.
3. Recall that the square root of a number \(a\) is a value \(b\) such that \(b^2 = a\).
4. Determine which number squared equals 16. Consider the positive and negative roots.
5. Conclude that the principal square root of 16 is the positive number that satisfies the equation.

Key Concepts

Exponents and Radicals

Exponents represent repeated multiplication of a base number. The expression 16^(1/2) indicates the square root of 16, which is a fundamental concept in algebra. Understanding how to manipulate exponents and their relationship to roots is essential for evaluating expressions involving fractional exponents.

Square Roots

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, since 4 * 4 = 16. Recognizing perfect squares and their roots is crucial for simplifying expressions and solving equations in algebra.

Properties of Exponents

The properties of exponents, such as the product of powers and power of a power, help simplify expressions involving exponents. In the case of fractional exponents, understanding that a^(m/n) equals the n-th root of a raised to the m-th power is vital for evaluating expressions like 16^(1/2). This knowledge allows for efficient computation and manipulation of algebraic expressions.