step 1 All right, guys, for 22, I need to simplify the expression of negative 2, w to the negative 5 to

(-2 w^-5)^3 | Numerade

Name: Problem 22, Chapter 5: Algebra for College Students
Uploaded: 2020-04-19T20:13:41-08:00
Duration: 36 s
Channel: Coach Rye
Description: (-2 w^-5)^3

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Key Concepts

Exponentiation of Negative Numbers

When raising negative numbers to a power, it is important to consider the parity of the exponent. An even exponent will result in a positive outcome, while an odd exponent will preserve the negative sign, a concept that directly impacts the simplification and evaluation of expressions.

Exponentiation of a Product

This concept refers to applying an exponent to a product of factors, meaning that the exponent distributes over each factor in the product. For instance, (ab)^n is equivalent to a^n multiplied by b^n, which is essential for breaking down and simplifying expressions like the one provided.

Power Rule for Exponents

The power rule for exponents states that when an expression with an exponent is raised to another power, the exponents multiply. This rule, expressed as (a^m)^n = a^(m*n), is fundamental in simplifying expressions where exponents are nested.

Negative Exponents

Negative exponents indicate that the base should be taken as the reciprocal and raised to the corresponding positive exponent. This concept is crucial in rewriting expressions by converting negative exponents to positive ones, aiding in further simplification.

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