Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent nonzero real numbers. See Examples 5 and 6. x^12/x^8

Key Concepts

Exponent Rules

Exponent rules are fundamental principles that govern the operations involving powers of numbers or variables. One key rule is that when dividing like bases, you subtract the exponents: a^m / a^n = a^(m-n). This rule is essential for simplifying expressions with exponents, as it allows for the reduction of terms efficiently.

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the opposite positive exponent. For example, a^(-n) = 1/a^n. In the context of simplification, it is important to express answers without negative exponents, which means converting any negative exponent terms into their positive reciprocal forms.

Nonzero Variables

In algebra, it is often assumed that variables represent nonzero real numbers to avoid undefined expressions, such as division by zero. This assumption is crucial when simplifying expressions with exponents, as it ensures that all operations are valid and that the results remain within the realm of real numbers.