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

Verified step by step guidance

1. Identify the base and the exponent in the expression. Here, the base is 3 and the exponent is 4.
2. Calculate the power by raising the base to the exponent: \(3^4\).
3. Multiply the result of \(3^4\) by -2, as indicated by the expression \(-2 \cdot 3^4\).
4. Remember that the negative sign outside the multiplication affects the entire product.
5. Combine the results from the previous steps to simplify the expression.

Key Concepts

Exponents

Exponents represent repeated multiplication of a number by itself. For example, in the expression 3⁴, the base 3 is multiplied by itself four times (3 × 3 × 3 × 3), resulting in 81. Understanding how to evaluate exponents is crucial for simplifying expressions that involve powers.

Multiplication of Integers

Multiplication of integers involves combining whole numbers to find their product. In the expression -2 • 3⁴, the negative integer -2 is multiplied by the result of 3⁴. This concept is essential for correctly applying the rules of multiplication, especially when dealing with positive and negative numbers.

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 acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. In evaluating -2 • 3⁴, one must first calculate the exponent before performing the multiplication.