Evaluate each expression. (4-2³)(-2+√25)

Verified step by step guidance

1. First, evaluate the exponent in the expression: calculate \$2^3\( which means \)2\( raised to the power of \)3$.
2. Next, perform the subtraction inside the first parentheses: compute \$4 - 2^3$ using the value found in the previous step.
3. Then, evaluate the square root in the second parentheses: calculate \(\sqrt{25}\), which is the number that when squared gives \$25$.
4. After that, perform the addition inside the second parentheses: compute \(-2 + \sqrt{25}\) using the value from the previous step.
5. Finally, multiply the results from the two parentheses together to find the value of the entire expression \((4 - 2^3)(-2 + \sqrt{25})\).

Key Concepts

Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed to ensure consistent results. It follows the PEMDAS/BODMAS rules: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Applying this correctly is essential to evaluate expressions accurately.

Exponents

Exponents represent repeated multiplication of a base number. For example, 2³ means 2 multiplied by itself three times (2 × 2 × 2 = 8). Understanding how to calculate powers is crucial when evaluating expressions involving exponents.

Square Roots

The square root of a number is a value that, when multiplied by itself, gives the original number. For instance, √25 equals 5 because 5 × 5 = 25. Recognizing and simplifying square roots helps in evaluating expressions involving radicals.