For Exercises, simplify. ((6 x^-4 y z^-1)/(14 x y^-4 z^2))^-3

Name: Problem 104, Chapter 9: Prealgebra and Introductory Algebra
Uploaded: 2020-06-22T16:53:32-08:00
Duration: 3 min 22 s
Channel: James Kiss
Description: For Exercises, simplify. ((6 x^-4 y z^-1)/(14 x y^-4 z^2))^-3

step 1 If we have 6x to the negative 4 times y times z to the negative 1st, over 14x times y to the neg

For Exercises, simplify. ((6 x^-4 y z^-1)/(14 x y^-4...

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Key Concepts

Exponent Rules

Exponent rules provide the guidelines for operations involving powers, such as multiplying or dividing like bases and raising a power to another power. These rules are fundamental for simplifying expressions where terms with exponents are combined, ensuring consistency in the manipulation of algebraic expressions.

Negative Exponents

Negative exponents indicate reciprocals in an expression. Instead of representing repeated division, a negative exponent signals that the corresponding base should be moved to the denominator (or vice versa) and made positive, which is a crucial step in rewriting and simplifying expressions.

Power of a Fraction

The power of a fraction rule states that when a fraction is raised to an exponent, both the numerator and the denominator are raised to that power. This rule is essential for simplifying expressions where an entire rational expression is subject to exponentiation.

Simplification of Rational Expressions

Simplifying rational expressions involves reducing fractions that have algebraic expressions in both the numerator and the denominator by canceling common factors and applying exponent rules. This process is key to rewriting complex expressions in their simplest form.

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