Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent nonzero real numbers. See Examples 5 and 6. 4r^-3/6r^-6

Key Concepts

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the absolute value of the exponent. For example, r^-n can be rewritten as 1/r^n. Understanding this concept is crucial for simplifying expressions that contain negative exponents, as it allows for the transformation of the expression into a more manageable form.

Simplifying Fractions

Simplifying fractions involves reducing the numerator and denominator to their lowest terms. This process often includes factoring out common factors and canceling them. In the context of algebraic expressions, it is essential to identify and eliminate common variables and coefficients to achieve a simpler form.

Properties of Exponents

The properties of exponents, such as the product of powers and the quotient of powers, provide rules for manipulating expressions with exponents. For instance, when dividing like bases, you subtract the exponents (a^m / a^n = a^(m-n)). Mastery of these properties is vital for correctly simplifying expressions involving multiple terms with exponents.