Question

Simplify. $\left(\frac{2 x w^{-3}}{3 x^{-4} w}\right)^{-2}$

   Simplify.
$\left(\frac{2 x w^{-3}}{3 x^{-4} w}\right)^{-2}$

Intermediate Algebra : Concepts and Applications

Intermediate Algebra : Concepts and Applications

Marvin L. Bittinger,… 10th Edition

Chapter 8, Problem 58

Instant Answer

Solved by Expert Ankit Gupta

07/24/2020

Step 1

This gives us: \[\left(\frac{2}{3} \cdot x^{1-(-4)} \cdot w^{-3-1}\right)^{-2} = \left(\frac{2}{3} \cdot x^{5} \cdot w^{-4}\right)^{-2}\] Show more…

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Simplify. $\left(\frac{2 x w^{-3}}{3 x^{-4} w}\right)^{-2}$

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Key Concepts

Exponent Laws

Exponent laws are fundamental tools in algebra that apply rules for the manipulation of powers. These include the product rule (adding exponents when multiplying like bases), the quotient rule (subtracting exponents when dividing like bases), and the power rule (multiplying exponents when raising a power to another power). These laws allow for the systematic simplification of expressions with exponents.

Negative Exponents

Negative exponents indicate the reciprocal of a base raised to the corresponding positive exponent. Instead of writing a base with a negative exponent, one can express it as the reciprocal of the same base with a positive exponent, thereby simplifying the expression and making calculations more transparent.

Power of a Product and Quotient

The power of a product or quotient rule states that when a product or quotient is raised to an exponent, each factor in the product or each term in the quotient is raised to that exponent. This helps distribute the power across the terms within parentheses and is crucial to accurately simplifying complex expressions involving multiple factors or fractions.

Simplifying Algebraic Expressions

Simplifying algebraic expressions involves combining like terms, applying exponent rules, and reducing complex expressions into simpler forms. This process makes it easier to analyze and solve problems by reducing expressions to their most basic form while retaining equivalence.

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