Evaluate.

[tex](-2-2)^2+\left(\frac{-4}{4}\right)^3[/tex]

Simplify the expressions inside the parentheses: ( − 2 − 2 ) = − 4 and ( 4 − 4 ​ ) = − 1 .
Evaluate the exponents: ( − 4 ) 2 = 16 and ( − 1 ) 3 = − 1 .
Add the results: 16 + ( − 1 ) = 15 .
The final answer is 15 ​ .

Explanation

Problem Analysis We are asked to evaluate the expression ( − 2 − 2 ) 2 + ( 4 − 4 ​ ) 3 . To do this, we will first simplify the expressions inside the parentheses, then evaluate the exponents, and finally add the results.

Simplifying Parentheses First, let's simplify the expressions inside the parentheses: − 2 − 2 = − 4 4 − 4 ​ = − 1

Substituting Values Now, substitute these values back into the original expression: ( − 4 ) 2 + ( − 1 ) 3

Evaluating Exponents Next, evaluate the exponents: ( − 4 ) 2 = ( − 4 ) × ( − 4 ) = 16 ( − 1 ) 3 = ( − 1 ) × ( − 1 ) × ( − 1 ) = − 1

Adding the Results Finally, add the results: 16 + ( − 1 ) = 16 − 1 = 15

Final Answer Therefore, the value of the expression is 15.


Examples
Understanding how to evaluate expressions with exponents and parentheses is crucial in many areas, such as physics and engineering. For example, when calculating the trajectory of a projectile, you need to evaluate expressions involving initial velocity, launch angle, and gravitational acceleration. These expressions often involve exponents and parentheses, and correctly evaluating them is essential for accurate predictions. Similarly, in electrical engineering, calculating power dissipation in a circuit involves evaluating expressions with squares and fractions, where the order of operations is critical.

Answered by GinnyAnswer | 2025-07-05