7 \times(-3) \times(-2)^2=?
Answer (1)
First, evaluate the exponent: ( − 2 ) 2 = 4 .
Then, multiply 7 by − 3 : 7 × − 3 = − 21 .
Multiply the result by 4 : − 21 × 4 = − 84 .
The final answer is − 84 .
Explanation
Understanding the Expression We are asked to evaluate the expression 7 × ( − 3 ) × ( − 2 ) 2 . Let's break it down step by step.
Evaluating the Exponent First, we need to evaluate ( − 2 ) 2 . This means ( − 2 ) × ( − 2 ) , which equals 4. So, we have 7 × ( − 3 ) × 4 .
Multiplying 7 and -3 Next, let's multiply 7 by − 3 . This gives us − 21 . Now our expression is − 21 × 4 .
Final Multiplication Finally, we multiply − 21 by 4 . This gives us − 84 . Therefore, 7 × ( − 3 ) × ( − 2 ) 2 = − 84 .
Selecting the Correct Option The correct option is C) -84.
Examples
Understanding how to evaluate expressions with negative numbers and exponents is crucial in many areas, such as calculating financial losses and gains, determining temperature changes, or even in physics when dealing with forces in opposite directions. For example, if a business loses 3 p er d a y f or 7 d a ys , an d t hi s l oss i s t h e na ff ec t e d b y a f a c t oro f (-2)^2$ due to market volatility, the total loss can be calculated using the same expression. This skill helps in making informed decisions by accurately quantifying the impact of various factors.
