Simplify each exponential expression in Exercises 23–64. (3x^4)(2x^7)

Key Concepts

Exponential Rules

Exponential rules are fundamental properties that govern the manipulation of expressions involving exponents. Key rules include the product of powers rule, which states that when multiplying two expressions with the same base, you add their exponents. For example, a^m * a^n = a^(m+n). Understanding these rules is essential for simplifying expressions like (3x^4)(2x^7).

Combining Like Terms

Combining like terms is a process used in algebra to simplify expressions by merging terms that have the same variable raised to the same power. In the expression (3x^4)(2x^7), the coefficients (3 and 2) can be multiplied together, while the variable parts can be simplified using the product of powers rule. This concept is crucial for achieving a simplified form of the expression.

Coefficient Multiplication

Coefficient multiplication involves multiplying the numerical factors (coefficients) of algebraic expressions. In the expression (3x^4)(2x^7), the coefficients 3 and 2 are multiplied to yield 6. This step is important in the simplification process, as it contributes to the final numerical value of the expression while maintaining the variable part.