In Exercises 1–14, multiply using the product rule. b⁴•b⁷

Verified step by step guidance

1. Identify the base of the terms: Both terms have the base 'b'.
2. Apply the product rule for exponents: When multiplying like bases, add the exponents.
3. Write the expression using the product rule: b^{4+7}.
4. Simplify the exponent: Add 4 and 7.
5. Express the final result as a single power of b.

Key Concepts

Product Rule of Exponents

The product rule of exponents states that when multiplying two expressions with the same base, you add their exponents. For example, a^m * a^n = a^(m+n). This rule simplifies calculations involving powers and is fundamental in algebra, especially when dealing with polynomial expressions.

Base of an Exponent

In exponential expressions, the base is the number that is being raised to a power. In the expression b⁴, 'b' is the base, and 4 is the exponent. Understanding the role of the base is crucial for applying exponent rules correctly, as operations depend on the base being consistent across terms.

Simplifying Exponential Expressions

Simplifying exponential expressions involves applying exponent rules to reduce the expression to its simplest form. This includes combining like terms, using the product rule, and ensuring that the final expression is expressed with the smallest possible exponents. Mastery of simplification is essential for solving more complex algebraic problems.