Evaluate each expression. See Example 4. -2 • 3⁴

Verified step by step guidance

1. Identify the components of the expression: the base number is -2 and the exponentiation part is 3 raised to the power of 4, written as \$3^4$.
2. Recall the order of operations (PEMDAS/BODMAS), which tells us to evaluate exponents before multiplication. So, first calculate \$3^4$.
3. Express \$3^4$ as \(3 \times 3 \times 3 \times 3\) to understand the repeated multiplication involved.
4. After finding the value of \$3^4$, multiply the result by -2, as indicated by the expression \(-2 \cdot 3^4\).
5. Write the final expression as \(-2 \times (3^4)\) and perform the multiplication to get the evaluated result.

Key Concepts

Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed. Exponents are evaluated before multiplication and addition. This ensures consistent and correct results when simplifying expressions like -2 • 3⁴.

Exponents

Exponents represent repeated multiplication of a base number. For example, 3⁴ means multiplying 3 by itself four times (3 × 3 × 3 × 3). Understanding how to calculate powers is essential for evaluating expressions involving exponents.

Multiplication of Integers

Multiplying integers involves combining their values while considering their signs. A negative number multiplied by a positive number results in a negative product. This concept is important when multiplying -2 by the value of 3⁴.