Evaluate each expression 16^1/2.

Verified step by step guidance

1. Recognize that the expression \$16^{1/2}\( represents the square root of 16 because an exponent of \)1/2$ means the square root.
2. Rewrite the expression using the square root notation: \(16^{1/2} = \sqrt{16}\).
3. Recall that the square root of a number is a value that, when multiplied by itself, gives the original number.
4. Identify the number that when squared equals 16. Since \(4 \times 4 = 16\), the square root of 16 is 4.
5. Therefore, \$16^{1/2}$ simplifies to 4.

Key Concepts

Exponents and Powers

Exponents indicate how many times a base number is multiplied by itself. For example, 16^2 means 16 multiplied by itself twice. Understanding exponents helps in simplifying expressions involving powers.

Fractional Exponents

A fractional exponent like 16^(1/2) represents a root; specifically, the denominator of the fraction is the root's degree. Here, 1/2 means the square root, so 16^(1/2) equals the square root of 16.

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 because 4 × 4 = 16. This concept is essential for evaluating expressions with fractional exponents.