Simplify $20+5^2 \times 2$
Answer (2)
First, calculate the exponent: 5 2 = 25 .
Then, perform the multiplication: 25 × 2 = 50 .
Finally, do the addition: 20 + 50 = 70 .
The simplified expression is 70 .
Explanation
Understanding the Expression We are asked to simplify the expression 20 + 5 2 "."2 . To do this, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This tells us the order in which we should perform the operations.
Evaluating the Exponent First, we evaluate the exponent. We have 5 2 = 5 × 5 = 25 . So our expression becomes 20 + 25 × 2 .
Performing the Multiplication Next, we perform the multiplication. We have 25 × 2 = 50 . So our expression becomes 20 + 50 .
Performing the Addition Finally, we perform the addition. We have 20 + 50 = 70 . Therefore, the simplified expression is 70.
Examples
Understanding the order of operations is crucial in many real-life scenarios, such as calculating finances or determining the outcome of a scientific experiment. For example, if you are calculating the total cost of items with discounts and taxes, you need to apply the discount before calculating the tax. Similarly, in programming, the order of operations determines how expressions are evaluated, which can affect the program's output. Mastering the order of operations ensures accurate and consistent results in various fields.
To simplify 20 + 5 2 × 2 , first evaluate the exponent to get 25 , then multiply 25 × 2 to get 50 , and finally add 20 + 50 to obtain 70 . The simplified expression is 70 .
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