Evaluate each expression. -2^4

Verified step by step guidance

1. Understand the expression: The expression is \(-2^4\).
2. Identify the base and the exponent: Here, the base is \(-2\) and the exponent is \(4\).
3. Apply the order of operations: According to the order of operations (PEMDAS/BODMAS), exponents are evaluated before multiplication or negation.
4. Evaluate the exponent: Calculate \(2^4\), which means multiplying 2 by itself 4 times.
5. Apply the negative sign: After calculating \(2^4\), apply the negative sign to the result.

Key Concepts

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. In the expression -2^4, the exponentiation is performed before applying the negative sign.

Exponents

Exponents represent repeated multiplication of a number by itself. For example, 2^4 means 2 multiplied by itself four times (2 × 2 × 2 × 2), which equals 16. Understanding how to handle exponents is crucial for evaluating expressions involving powers, especially when negative bases are involved.

Negative Numbers

Negative numbers are values less than zero and are represented with a minus sign. When evaluating expressions with negative bases, it is important to distinguish between the negative sign and the exponent. In the case of -2^4, the exponent applies only to the 2, resulting in a positive 16, and then the negative sign is applied, yielding -16.