Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (p^4/q)^2

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 quotient of powers (a^m / a^n = a^(m-n)). Understanding these rules is essential for simplifying expressions with exponents.

Simplifying Rational Expressions

Simplifying rational expressions involves reducing fractions to their simplest form by canceling common factors in the numerator and denominator. This process often requires factoring polynomials and applying the rules of exponents to ensure that the expression is expressed in the most concise manner possible.

Nonzero Variables

In algebra, assuming that variables represent nonzero real numbers is crucial for avoiding undefined expressions, particularly in division. This assumption allows for the application of exponent rules without concern for division by zero, ensuring that the simplification process remains valid and applicable in real-world scenarios.