Perform the indicated operation: [tex]7+\left(3^2+4^2\right)^2-150[/tex]
[tex]\begin{array}{l}
7+(\square+\square)^2-150 \\
7+(\square)-150 \\
7+\square-150
\end{array}[/tex]
Answer (2)
The evaluation of the expression 7 + ( 3 2 + 4 2 ) 2 − 150 results in 482 after performing the calculations step-by-step according to the order of operations. We first evaluated the squares, then added, squared the result, and finally added and subtracted as required.
;
Evaluate the squares inside the parentheses: 3 2 = 9 and 4 2 = 16 .
Add the results inside the parentheses: 9 + 16 = 25 .
Square the result: 2 5 2 = 625 .
Perform the remaining addition and subtraction: 7 + 625 − 150 = 482 .
The final result is 482 .
Explanation
Understanding the expression We are asked to evaluate the expression 7 + ( 3 2 + 4 2 ) 2 − 150 . We will follow the order of operations (PEMDAS) to simplify the expression.
Evaluating the parentheses First, we evaluate the expression inside the parentheses. We have 3 2 = 3 × 3 = 9 and 4 2 = 4 × 4 = 16 . So, 3 2 + 4 2 = 9 + 16 = 25 .
Evaluating the exponent Now, we substitute this result back into the original expression: 7 + ( 25 ) 2 − 150 . Next, we evaluate the exponent: 2 5 2 = 25 × 25 = 625 .
Performing the addition Now, we substitute this result back into the expression: 7 + 625 − 150 . Next, we perform the addition: 7 + 625 = 632 .
Performing the subtraction Finally, we perform the subtraction: 632 − 150 = 482 . Therefore, the value of the expression is 482.
Examples
Understanding order of operations is crucial in many real-life scenarios, such as calculating the total cost of items with discounts and taxes. For example, imagine you are buying a video game that costs $50, has a 10% discount, and then a 6% sales tax is applied. The expression to calculate the final price would be 50 − ( 0.10 × 50 ) + ( 0.06 × ( 50 − ( 0.10 × 50 ))) . By following the order of operations, you can accurately determine the final cost of the video game. This skill is also useful in budgeting, financial planning, and understanding complex formulas in science and engineering.
