Determine whether each statement is true or false. If false, correct the right side of the equation. (3x^2)^-1 = 3x^-2

Exponents represent repeated multiplication of a base number. A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent. For example, x^-n = 1/x^n. Understanding this concept is crucial for manipulating expressions involving negative exponents correctly.

The properties of exponents include rules such as the product of powers, power of a power, and the power of a product. These rules help simplify expressions involving exponents. For instance, (a^m)^n = a^(m*n) and (ab)^n = a^n * b^n. Applying these properties correctly is essential for solving equations involving exponents.

Simplifying algebraic expressions involves combining like terms and applying the rules of exponents to rewrite expressions in a more manageable form. This process often includes factoring, distributing, and reducing fractions. Mastery of simplification techniques is necessary to accurately assess the truth of algebraic statements and equations.