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Chapter 0: Problem 12

Evaluate the expressions. $$ 3 \cdot(-2)^{0} $$

Short Answer

Expert verified
The expression \(3 \cdot(-2)^{0}\) simplifies as follows: Calculate the exponent first, \((-2)^{0} = 1\), and then perform the multiplication, \(3 \cdot 1 = 3\). The final answer is \(3\).

Step by step solution

01

Identify the Order of Operations

To evaluate the given expression, we need to follow the order of operations: 1. Parentheses 2. Exponents 3. Multiplication and Division (left to right) 4. Addition and Subtraction (left to right) Our expression only includes an exponent and multiplication, so we'll be focusing on steps 2 and 3.
02

Compute the Exponent

According to the order of operations, we start with the exponent: \((-2)^{0}\) Any non-zero number raised to the power of 0 is equal to 1. Therefore, \((-2)^{0} = 1\).
03

Perform the Multiplication

Now that we have calculated the exponent, the expression becomes: $$ 3 \cdot 1 $$ This is a simple multiplication: \(3 \cdot 1 = 3\).
04

Write the Final Answer

The given expression simplifies to the following value: $$ 3 \cdot(-2)^{0} = 3 $$ Therefore, the expression evaluates to 3.

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