Evaluate each expression. (5-3²)(√16-2³)

Verified step by step guidance

1. First, evaluate the exponent in the expression: calculate \$3^2\( and \)2^3$ separately.
2. Next, substitute these values back into the expression to simplify inside the parentheses: \((5 - 3^2)\) becomes \((5 - \text{value})\) and \((\sqrt{16} - 2^3)\) becomes \((\sqrt{16} - \text{value})\).
3. Then, evaluate the square root \(\sqrt{16}\).
4. After that, perform the subtraction inside each set of parentheses to simplify both expressions.
5. Finally, multiply the two simplified results together to get the value of the entire expression.

Key Concepts

Order of Operations

The order of operations is a set of rules that dictate the sequence in which mathematical operations should be performed to ensure consistent results. It is commonly remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Applying this order correctly is essential to evaluate expressions accurately.

Exponents

Exponents represent repeated multiplication of a base number. For example, 3² means 3 multiplied by itself (3 × 3 = 9). Understanding how to calculate powers is crucial for simplifying expressions involving exponents before performing other operations.

Square Roots

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 and simplifying square roots is important when evaluating expressions that include radical signs.