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

Verified step by step guidance

1. Understand the difference between the expressions with and without parentheses, as this affects the order of operations and the sign of the result.
2. For part a, calculate \$8^2$ by multiplying 8 by itself: \(8 \times 8\).
3. For part b, interpret \(-8^2\) as the negative of \$8^2\(, so first calculate \)8^2$ and then apply the negative sign.
4. For part c, calculate \((-8)^2\) by squaring the entire quantity inside the parentheses, meaning multiply \(-8\) by \(-8\).
5. For part d, evaluate \(-(-8)^2\) by first calculating \((-8)^2\) and then applying the negative sign outside the expression.

Key Concepts

Order of Operations (PEMDAS)

The order of operations dictates the sequence in which mathematical operations are performed. Exponents are evaluated before multiplication, division, addition, or subtraction. Understanding this helps correctly interpret expressions like -8², where the exponent applies before the negative sign.

Exponents and Powers

An exponent indicates how many times a base number is multiplied by itself. For example, 8² means 8 × 8 = 64. Recognizing how to apply exponents to positive and negative bases is essential for evaluating expressions like (-8)² versus -8².

Negative Signs and Grouping Symbols

Parentheses affect how negative signs interact with exponents. (-8)² means the entire negative number is squared, resulting in a positive value, while -8² means the negative sign is separate and applied after squaring 8. Proper use of grouping symbols clarifies the intended calculation.