Question

Simplify the expression. $4 x \cdot\left(-x \cdot x^{3}\right)^{2}$

   Simplify the expression.
$4 x \cdot\left(-x \cdot x^{3}\right)^{2}$

Algebra 1: Concepts and Skills

Algebra 1: Concepts and Skills

Ron Larson, Laurie… 1st Edition

Chapter 8, Problem 58

Instant Answer

Solved by Expert Cory Kuzinski

04/18/2020

Step 1

We have $-x \cdot x^{3}$ which is $-x^{4}$ because when we multiply expressions with the same base, we add the exponents. So, the expression becomes $4x \cdot (-x^{4})^{2}$. Show more…

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Simplify the expression. $4 x \cdot\left(-x \cdot x^{3}\right)^{2}$

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Key Concepts

Properties of Exponents

This concept involves the rules governing how exponents are manipulated in expressions. It includes understanding how to multiply similar bases by adding exponents, raising a power to another power by multiplying exponents, and applying the power of a product rule, which states that each factor in a product can be separately raised to an exponent.

Even Powers and Negative Factors

When raising an expression to an even power, any negative factors become positive because multiplying an even number of negative signs results in a positive sign. This principle simplifies expressions involving negatives when they are squared or raised to another even exponent.

Multiplying Monomials

This key concept involves combining monomials by multiplying their coefficients and applying the laws of exponents to like bases. It allows for the simplification of algebraic expressions by merging terms with the same base, thus streamlining the overall expression.

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