Question

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

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

Elementary Algebra

Elementary Algebra

Lynn Marecek 2nd Edition

Chapter 6, Problem 152

Instant Answer

Solved by Expert Sherrie Fenner

07/15/2021

Step 1

Here, $a$ is $2mn^4$ and $n$ is $5$. So we have: $$(2 m n^{4})^{5} = 2^5 m^5 (n^4)^5$$ Show more…

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

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Key Concepts

Power of a Product Rule

The power of a product rule states that when a product of factors is raised to an exponent, each factor can be raised to the exponent independently. In algebraic terms, (ab)^n is equal to a^n multiplied by b^n, which allows for the separation and simplification of complex algebraic expressions.

Power of a Power Rule

The power of a power rule is used when an exponentiated term is raised to another exponent. According to this rule, (a^m)^n is simplified by multiplying the exponents together to result in a^(m*n). This rule streamlines the simplification process of expressions with multiple layers of exponents.

Exponentiation

Exponentiation is the process of raising a number, variable, or expression to a power, which represents repeated multiplication. It is a fundamental operation in algebra that involves multiplying the base by itself as many times as indicated by the exponent.

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