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

Verified step by step guidance

1. Identify the components of the expression: the base -2 and the exponent 3 raised to the power 4, written as \(-2 \cdot 3^{4}\).
2. Recall the order of operations (PEMDAS/BODMAS): exponents are evaluated before multiplication.
3. Calculate the exponent part first: evaluate \$3^{4}$, which means multiplying 3 by itself 4 times.
4. After finding the value of \$3^{4}$, 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 final value.

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

Multiplication of integers involves combining numbers with positive or negative signs. Multiplying a negative number by a positive number results in a negative product. This concept is important when multiplying -2 by the value of 3⁴.