Evaluate the expression: $-(8-12)+6^0+(-4)^2$
Answer (1)
Evaluate the expression inside the parenthesis: 8 − 12 = − 4 .
Simplify the first term: − ( − 4 ) = 4 .
Evaluate the exponential term: 6 0 = 1 .
Evaluate the squared term: ( − 4 ) 2 = 16 .
Combine the results: 4 + 1 + 16 = 21 .
The final answer is 21 .
Explanation
Understanding the Expression We are asked to evaluate the expression − ( 8 − 12 ) + 6 0 + ( − 4 ) 2 . Let's break it down step by step.
Evaluating Parenthesis First, we evaluate the expression inside the parenthesis: 8 − 12 = − 4 .
Simplifying the First Term Next, we have − ( 8 − 12 ) = − ( − 4 ) = 4 .
Evaluating the Exponential Term Then, we evaluate 6 0 . Any non-zero number raised to the power of 0 is 1, so 6 0 = 1 .
Evaluating the Squared Term Finally, we evaluate ( − 4 ) 2 . This means ( − 4 ) × ( − 4 ) = 16 .
Combining the Results Now, we substitute these values back into the original expression: − ( 8 − 12 ) + 6 0 + ( − 4 ) 2 = 4 + 1 + 16 = 21 .
Final Answer Therefore, the value of the expression is 21.
Examples
Understanding how to evaluate expressions with exponents and parentheses is a fundamental skill in algebra. In real life, this skill is useful in various scenarios, such as calculating the future value of an investment with compound interest, determining the trajectory of a projectile in physics, or even optimizing resource allocation in business. For example, if you invest $100 at an annual interest rate of 5% compounded annually, after 3 years, the future value can be calculated using the expression 100 ( 1 + 0.05 ) 3 , which requires evaluating exponents and parentheses.
