Concept Check Evaluate each exponential expression.a. 8²b. -8²c. (-8)²d. -(-8)²

Verified step by step guidance

1. Step 1: Understand the concept of exponents. An exponent indicates how many times a number, known as the base, is multiplied by itself.
2. Step 2: For part (a), 8², calculate 8 multiplied by itself.
3. Step 3: For part (b), -8², recognize that the negative sign is not included in the base, so calculate 8² first and then apply the negative sign.
4. Step 4: For part (c), (-8)², note that the negative sign is included in the base, so multiply -8 by itself.
5. Step 5: For part (d), -(-8)², first calculate (-8)² as in part (c), then apply the negative sign to the result.

Key Concepts

Exponential Notation

Exponential notation is a mathematical shorthand that represents repeated multiplication of a number by itself. For example, in the expression 8², the base 8 is multiplied by itself, resulting in 64. Understanding how to interpret and calculate exponential expressions is crucial for evaluating them 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 acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. This concept is essential for evaluating expressions with multiple operations, such as those involving exponents and negative signs.

Negative Numbers and Squaring

When squaring a negative number, the result is always positive because multiplying two negative numbers yields a positive product. For instance, (-8)² equals 64, while -8² is interpreted as -(8²), resulting in -64. Understanding how to handle negative signs in conjunction with exponents is vital for accurately evaluating expressions.