Simplify the given expressions using the order of operations...

Simplify the given expressions using the order of operations and exponent rules. Provide reasons for each step. Write each answer without negative exponents.
$$\frac{-240 m^{-2} n^{-4}}{60 m^{-5} n^{3}}$$

Key Concepts

Simplifying Rational Expressions

This concept involves reducing fractions that contain polynomials or monomials by factoring common terms and canceling them. The process typically includes working with both numerical coefficients and variables with exponents, ensuring the final expression is as simple and compact as possible without negative exponents.

Order of Operations

This concept involves following a hierarchical sequence when performing calculations, typically remembered as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). It ensures that the operations in an expression are processed in the correct order, which is crucial for both numerical and algebraic expressions.

Properties of Exponents

This concept includes several rules for manipulating expressions with exponents, such as the product rule, quotient rule, and power rule. In the context of division, the quotient rule states that when dividing like bases, you subtract the exponent in the denominator from the exponent in the numerator, which simplifies the expression.

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the corresponding positive exponent. Cleaning up expressions by rewriting negative exponents as positive ones (by taking reciprocals) is an essential technique in algebra to obtain a simplified standard form of an expression.

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