Question

Simplify each expression. $$\left(3 m^{2} n\right)^{2}\left(2 m n^{5}\right)^{4}$$

   Simplify each expression.
$$\left(3 m^{2} n\right)^{2}\left(2 m n^{5}\right)^{4}$$

Elementary Algebra

Elementary Algebra

Lynn Marecek 2nd Edition

Chapter 6, Problem 163

Instant Answer

Solved by Expert Sherrie Fenner

07/15/2021

Step 1

This gives us: $$(3 m^{2} n)^{2}(2 m n^{5})^{4} = 3^{2} m^{2*2} n^{2} * 2^{4} m^{4} n^{5*4}$$ Show more…

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Simplify each expression. $$\left(3 m^{2} n\right)^{2}\left(2 m n^{5}\right)^{4}$$

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Key Concepts

Product of Powers Rule

This concept involves combining terms that have the same base when they are multiplied together, by adding their exponents, expressed as a^m * a^n = a^(m+n). It provides a systematic way to simplify expressions involving multiplications of like bases.

Exponentiation of a Product

This concept refers to the rule that when a product is raised to a power, each factor in the product is raised to that power individually. It is expressed as (ab)^n = a^n * b^n, and is essential for simplifying expressions where a grouped product is raised to an exponent.

Power of a Power Rule

This rule states that when an exponential expression is raised to another power, the exponents are multiplied. In mathematical terms, (a^m)^n equals a^(m*n). This rule is particularly useful when dealing with nested exponents or simplifying expressions with multiple layers of powers.

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