In Exercises 1–20, use the product rule to multiply. _ _ ⁴√9 ⋅ ⁴√3

Key Concepts

Product Rule of Exponents

The product rule states that when multiplying two expressions with the same base, you can add their exponents. For example, a^m * a^n = a^(m+n). This rule is essential for simplifying expressions involving exponents, particularly when dealing with roots and fractional exponents.

Radical Expressions

Radical expressions involve roots, such as square roots or fourth roots. The expression ⁴√x represents the fourth root of x, which is the value that, when raised to the fourth power, equals x. Understanding how to manipulate and simplify radical expressions is crucial for solving problems involving roots.

Simplifying Radicals

Simplifying radicals involves reducing a radical expression to its simplest form. This can include factoring out perfect squares or higher powers from under the radical sign. For example, ⁴√(a*b) can be expressed as ⁴√a * ⁴√b, which is useful for applying the product rule effectively.