step 1 All right, guys, for 33, it wants me to go ahead and simplify the expression of negative 3A over

(-(3 a)/(4))^3 | Numerade

Name: Problem 33, Chapter 5: Algebra for College Students
Uploaded: 2020-04-19T20:20:32-08:00
Duration: 46 s
Channel: Coach Rye
Description: (-(3 a)/(4))^3

Key Concepts

Handling Negative Bases in Exponentiation

When a negative number or expression is raised to a power, the sign of the result depends on whether the exponent is even or odd. An odd exponent will yield a negative result, while an even exponent results in a positive outcome. This concept is important when working with algebraic expressions that include negative signs, ensuring the correct handling of signs during simplification.

Exponentiation

Exponentiation is the operation of raising a base to a power. It involves multiplying the base by itself as many times as indicated by the exponent. Understanding exponentiation is crucial in algebra because it allows you to simplify and manipulate expressions where variables and constants are raised to a power.

Power of a Product

The power of a product rule states that when an entire product is raised to an exponent, each factor in the product is raised to that exponent. This principle simplifies expressions by allowing you to distribute the exponent to both the numerical coefficients and any variables present in the product.

Raising Fractions to a Power

When a fraction is raised to a power, both the numerator and the denominator are raised to that power individually. This makes it possible to simplify expressions that involve fractional bases, by treating the numerator and denominator separately according to the exponent.

Transcript

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