Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (-5n^4/r^2)^3

Key Concepts

Exponent Rules

Exponent rules are fundamental principles that govern how to manipulate expressions involving powers. 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.

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the opposite positive exponent. For example, a^(-n) = 1/(a^n). This concept is crucial when simplifying expressions that involve negative powers, as it allows for the transformation of the expression into a more manageable form.

Simplifying Rational Expressions

Simplifying rational expressions involves reducing fractions to their simplest form by factoring and canceling common factors. This process is important when dealing with variables in the numerator and denominator, ensuring that the expression is expressed in the most concise way while maintaining its value.