Question

Simplify. $$\left(-5 m^{4} n^{6}\right)\left(8 m^{-5} n^{-3}\right)$$

   Simplify.
$$\left(-5 m^{4} n^{6}\right)\left(8 m^{-5} n^{-3}\right)$$

Elementary Algebra

Elementary Algebra

Lynn Marecek 2nd Edition

Chapter 6, Problem 541

Instant Answer

Solved by Expert Sherrie Fenner

07/19/2021

Step 1

This gives us: $$(-5 \times 8) \times (m^{4} \times m^{-5}) \times (n^{6} \times n^{-3})$$ Show more…

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Simplify. $$\left(-5 m^{4} n^{6}\right)\left(8 m^{-5} n^{-3}\right)$$

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Key Concepts

Simplification of Monomials

Simplifying monomials requires combining the multiplication of coefficients with the application of the product of powers rule for each variable. This overall process results in a more concise and standard form of the expression.

Negative Exponents

Negative exponents indicate that the base should be taken as the reciprocal raised to the corresponding positive exponent. Understanding this concept allows one to correctly simplify expressions even when some exponents are negative.

Multiplication of Coefficients

This concept involves multiplying the numerical parts (the constants) of the terms independently of the variables. It is a straightforward arithmetic multiplication which forms the foundation for simplifying algebraic expressions.

Product of Powers

When multiplying expressions with the same base, you add the exponents according to the rule a^m * a^n = a^(m+n). This property is essential for combining variables raised to a power in the process of simplification.

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