In Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (3x−4 y z−7)(3x)−3

Exponential rules are fundamental properties that govern the manipulation of expressions involving exponents. Key rules include the product of powers (a^m * a^n = a^(m+n)), the power of a power ( (a^m)^n = a^(m*n)), and the power of a product ( (ab)^n = a^n * b^n). Understanding these rules is essential for simplifying expressions with exponents.

The distributive property states that a(b + c) = ab + ac, allowing us to multiply a single term by two or more terms inside a parenthesis. This property is crucial when simplifying expressions, especially when dealing with products of sums or differences. It helps in breaking down complex expressions into simpler components for easier manipulation.

Negative exponents indicate the reciprocal of the base raised to the opposite positive exponent, expressed as a^(-n) = 1/(a^n). This concept is vital when simplifying expressions that contain negative exponents, as it allows for the transformation of terms into a more manageable form, often leading to a clearer final expression.