Evaluate each expression. See Example 4. -2⁴

Verified step by step guidance

1. Identify the expression to evaluate: \(-2^4\).
2. Recall the order of operations (PEMDAS/BODMAS): exponents are evaluated before multiplication or negation.
3. Evaluate the exponent first: calculate \$2^4$, which means \(2 \times 2 \times 2 \times 2\).
4. After finding \$2^4$, apply the negative sign in front of the result, since the negative sign is not inside the exponentiation.
5. Write the final expression as \(- (2^4)\) and simplify accordingly.

Key Concepts

Order of Operations (PEMDAS)

The order of operations dictates the sequence in which mathematical operations are performed: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). This ensures consistent and correct evaluation of expressions.

Exponents and Powers

An exponent indicates how many times a base number is multiplied by itself. For example, 4⁴ means 4 × 4 × 4 × 4. Understanding how to compute powers is essential for evaluating expressions involving exponents.

Negative Signs and Exponents

A negative sign before a base with an exponent can change the result depending on parentheses. For example, -2⁴ means the negative of 2⁴, which is -16, while (-2)⁴ means (-2) multiplied four times, resulting in 16. Recognizing this distinction is crucial.