Identify the operations within each set of parentheses: (5 - 3^2) and (\sqrt{16} - 2^3).
Calculate the exponent in the first set of parentheses: 3^2.
Calculate the square root and the exponent in the second set of parentheses: \sqrt{16} and 2^3.
Subtract the results of the operations inside each set of parentheses: (5 - result of 3^2) and (result of \sqrt{16} - result of 2^3).
Multiply the results of the two expressions obtained from the parentheses.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Order of Operations
The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. In evaluating expressions, it is crucial to follow these rules to arrive at the correct answer.
Exponents represent repeated multiplication of a number by itself. For example, 3² means 3 multiplied by itself, which equals 9. Understanding how to calculate exponents is essential for simplifying expressions that involve powers, as seen in the expression (5-3²).
The square root of a number is a value that, when multiplied by itself, gives the original number. For instance, √16 equals 4 because 4 × 4 = 16. Recognizing how to compute square roots is important for evaluating expressions that include radical signs, such as in the expression (√16-2³).