In Exercises 1–14, multiply using the product rule.x•x³

Verified step by step guidance

1. Identify the base and the exponents in the expression: The base is \(x\) and the exponents are 1 (for \(x\)) and 3 (for \(x^3\)).
2. Apply the product rule for exponents, which states that when multiplying like bases, you add the exponents: \(x^a \cdot x^b = x^{a+b}\).
3. Add the exponents: \(1 + 3\).
4. Rewrite the expression using the sum of the exponents: \(x^{1+3}\).
5. Simplify the expression to get the final result: \(x^4\).

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, x^a * x^b = x^(a+b). This rule simplifies the process of multiplying powers and is fundamental in algebraic manipulations involving exponents.

Exponent Notation

Exponent notation is a way to express repeated multiplication of a number by itself. For instance, x^3 means x multiplied by itself three times (x * x * x). Understanding this notation is crucial for performing operations involving powers and for interpreting algebraic expressions correctly.

Simplifying Expressions

Simplifying expressions involves reducing them to their most basic form, making them easier to work with. This often includes combining like terms and applying rules of exponents. Mastery of simplification techniques is essential for solving algebraic equations and performing calculations efficiently.