Simplify each expression. See Example 1. (4^2)(4^8)

Key Concepts

Exponential Rules

Exponential rules are mathematical principles that govern the operations involving exponents. One key rule is that when multiplying two expressions with the same base, you add their exponents. For example, a^m * a^n = a^(m+n). This rule is essential for simplifying expressions like (4^2)(4^8) by combining the exponents.

Base of an Exponent

The base of an exponent is the number that is raised to a power. In the expression 4^n, 4 is the base, and n is the exponent. Understanding the base is crucial because it determines the value of the expression when combined with the exponent. In the given expression, both terms share the same base of 4, allowing for simplification.

Simplification of Expressions

Simplification of expressions involves reducing a mathematical expression to its simplest form. This process often includes combining like terms, applying arithmetic operations, and using algebraic rules. In the context of the question, simplifying (4^2)(4^8) means applying the exponential rule to express the product as a single exponent, resulting in 4^(2+8) = 4^10.