Evaluate each expression. 169^1/2

Verified step by step guidance

1. Recognize that the expression \$169^{1/2}\( represents the square root of 169 because an exponent of \)1/2$ means the square root.
2. Rewrite the expression using the square root symbol: \(\sqrt{169}\).
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 which, when squared, equals 169. Think of perfect squares you know, such as \$13^2 = 169$.
5. Conclude that \(\sqrt{169} = 13\), so \$169^{1/2} = 13$.

Key Concepts

Rational Exponents

Rational exponents represent roots and powers combined. For example, an exponent of 1/2 means the square root of the base number. Understanding how to interpret and manipulate rational exponents is essential for evaluating expressions like 169^(1/2).

Square Roots

The square root of a number is a value that, when multiplied by itself, gives the original number. Since 169 is a perfect square, its square root is an integer. Recognizing perfect squares helps simplify expressions involving square roots quickly.

Evaluating Exponents

Evaluating exponents involves applying the power to the base number correctly. For fractional exponents, this means finding the appropriate root. Mastery of exponent rules allows for accurate simplification and evaluation of expressions like 169^(1/2).