Evaluate each expression 16^1/2.

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Recognize that the expression \(16^{1/2}\) represents the square root of 16 because an exponent of \(1/2\) means the square root.

Rewrite the expression using the square root notation: \(16^{1/2} = \sqrt{16}\).

Recall that the square root of a number is a value that, when multiplied by itself, gives the original number.

Identify the number that when squared equals 16. Since \(4 \times 4 = 16\), the square root of 16 is 4.

Therefore, \(16^{1/2}\) simplifies to 4.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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