Evaluate each expression. See Example 4. -2⁴

Verified step by step guidance

1. Recall the order of operations: exponents are evaluated before multiplication or applying a negative sign.
2. Rewrite the expression to clarify the exponentiation: the expression is \(-2^4\), which means the negative sign is applied after calculating \$2^4$.
3. Calculate the exponent part first: \$2^4$ means \(2 \times 2 \times 2 \times 2\).
4. After finding the value of \$2^4$, apply the negative sign in front of it.
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, 2⁴ means 2 × 2 × 2 × 2 = 16. Understanding how to compute powers is essential for evaluating expressions involving exponents.

Negative Signs and Exponents

When a negative sign precedes a base with an exponent, it is important to distinguish between -2⁴ and (-2)⁴. The expression -2⁴ means the negative of 2⁴, resulting in -16, while (-2)⁴ means (-2) multiplied four times, resulting in 16.