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

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First, evaluate the exponent in the expression: calculate \$2^3$ which means $2$ raised to the power of $3$.

Next, perform the subtraction inside the first parentheses: compute \$4 - 2^3$ using the value found in the previous step.

Then, evaluate the square root in the second parentheses: calculate $\sqrt{25}$, which is the number that when squared gives $25$.

After that, perform the addition inside the second parentheses: compute $-2 + \sqrt{25}$ using the value from the previous step.

Finally, multiply the results from the two parentheses together to find the value of the entire expression $(4 - 2^3)(-2 + \sqrt{25})$.

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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 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.

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