step 1 In this problem, we're being asked to multiply the monomial 4W squared by the trinomial 3W to th

Question

$\frac{\left(4 w^{3}\right)^{2}}{32 w}$

Name: Problem 77, Chapter 5: Elementary Algebra
Uploaded: 2020-04-17T01:32:40-08:00
Duration: 41 s
Channel: Julie Silva
Description: ((4 w^3)^2)/(32 w)

   $\frac{\left(4 w^{3}\right)^{2}}{32 w}$

Elementary Algebra

Laura Bracken, Ed… 1st Edition

Chapter 5, Problem 77

Instant Answer

Solved by Expert Julie Silva

04/17/2020

Step 1

First, we can simplify the expression inside the parentheses: $(4w^3)^2 = (4^2)(w^3)^2 = 16w^6$ Show more…

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$\frac{\left(4 w^{3}\right)^{2}}{32 w}$

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Key Concepts

Power of a Power Rule

This rule states that when you raise a power to another power, you multiply the exponents. It's fundamental in simplifying expressions where an entire term (including its coefficient and variable) is raised to an exponent.

Multiplication of Exponents

This concept involves adding the exponents when multiplying terms with the same base. It is essential in combining powers during the simplification of algebraic expressions.

Division of Exponents

When dividing terms with the same base, you subtract the exponent in the denominator from the exponent in the numerator. This is critical for reducing expressions that involve the division of exponential expressions.

Coefficient Simplification

This concept involves simplifying the numerical part of expressions independently from the variables. It typically uses standard arithmetic operations like multiplication or division to reduce the coefficients in algebraic terms.

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