In Exercises 59–70, evaluate each exponential expression. -10^2

Verified step by step guidance

1. Understand the expression: \(-10^2\) means \(-1\) times \(10^2\).
2. Recall the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
3. Apply the order of operations: First, calculate the exponent \(10^2\).
4. Calculate \(10^2\) which is \(10 \times 10\).
5. Multiply the result by \(-1\) to evaluate the expression \(-10^2\).

Key Concepts

Exponential Expressions

Exponential expressions involve a base raised to a power, indicating how many times the base is multiplied by itself. For example, in the expression a^n, 'a' is the base and 'n' is the exponent. Understanding how to evaluate these expressions is crucial for solving problems involving growth, decay, and other mathematical applications.

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 common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. In evaluating expressions like -10^2, recognizing that the exponent is applied before the negative sign is essential.

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the absolute value of the exponent. For instance, a^-n equals 1/a^n. While this concept is not directly applicable in the given expression, understanding it is important for broader contexts where negative exponents may appear, influencing how we interpret and simplify expressions.