Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (3^1/2)(3^3/2)

Key Concepts

Exponents and Their Properties

Exponents represent repeated multiplication of a base number. Key properties include the product of powers, which states that when multiplying like bases, you add the exponents. For example, a^m * a^n = a^(m+n). Understanding these properties is essential for simplifying expressions involving exponents.

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the opposite positive exponent. For instance, a^(-n) = 1/(a^n). In this problem, the instruction to write answers without negative exponents means we must express all terms in a positive exponent format, ensuring clarity and adherence to mathematical conventions.

Radicals and Rational Exponents

Radicals can be expressed as rational exponents, where the nth root of a number is represented as a fractional exponent. For example, the square root of a is written as a^(1/2). This concept is crucial for simplifying expressions that involve roots, as it allows for the application of exponent rules to combine and simplify terms effectively.