Evaluate each expression. 16^1/4

Verified step by step guidance

1. Recognize that the expression involves a fractional exponent: \(16^{\frac{1}{4}}\). This means you are finding the fourth root of 16.
2. Rewrite the expression using radical notation: \(16^{\frac{1}{4}} = \sqrt[4]{16}\).
3. Recall that the fourth root of a number is the value that, when raised to the power of 4, gives the original number.
4. Identify the number which, when raised to the 4th power, equals 16. Think about perfect powers of integers.
5. Express the final answer as the positive root that satisfies the equation \(x^4 = 16\).

Key Concepts

Rational Exponents

Rational exponents represent roots and powers simultaneously. For example, a^(m/n) means the nth root of a raised to the mth power. Understanding this allows you to rewrite expressions like 16^(1/4) as the fourth root of 16.

Evaluating Roots

Evaluating roots involves finding a number that, when raised to a specific power, equals the given value. For 16^(1/4), you find the number which raised to the 4th power equals 16, which is 2, since 2^4 = 16.

Properties of Exponents

Properties of exponents, such as the power of a power and product rules, help simplify expressions with exponents. Recognizing these properties aids in manipulating and evaluating expressions with fractional exponents correctly.