CONCEPT PREVIEW Evaluate each expression.10³

Verified step by step guidance

1. Identify the base and the exponent in the expression. Here, the base is 10 and the exponent is 3.
2. Understand that the exponent indicates how many times the base is multiplied by itself. In this case, 10 is multiplied by itself 3 times.
3. Write the expression as a multiplication of the base: \(10 \times 10 \times 10\).
4. Calculate the result of the multiplication step by step: first, multiply the first two 10s, then multiply the result by the third 10.
5. The final result is the value of \(10^3\).

Key Concepts

Exponents

Exponents are a mathematical notation indicating the number of times a number, known as the base, is multiplied by itself. For example, in the expression 10³, the base is 10 and the exponent is 3, meaning 10 is multiplied by itself three times (10 × 10 × 10). Understanding exponents is crucial for evaluating expressions involving powers.

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 10³, the exponentiation is performed before any other operations.

Base and Power Relationship

The relationship between a base and its power is fundamental in understanding how exponential expressions work. The base is the number being raised to a power, while the power indicates how many times the base is multiplied by itself. In the case of 10³, the base is 10, and the power of 3 signifies that 10 is used as a factor three times, resulting in 1000.