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(-z^5)^2(-z^7)^3 | Numerade

Name: Problem 66, Chapter 5: Elementary Algebra
Uploaded: 2021-02-24T07:54:53-08:00
Duration: 1 min 1 s
Channel: Narayan Hari
Description: (-z^5)^2(-z^7)^3

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Key Concepts

Exponentiation

Exponentiation is the mathematical operation involving two numbers, the base and the exponent. It represents repeated multiplication of the base by itself as many times as indicated by the exponent, which is fundamental to simplifying expressions involving powers.

Power of a Product Rule

The power of a product rule states that when a product of several factors is raised to an exponent, each factor can be raised to that exponent individually. This rule is crucial for breaking down and simplifying expressions where both numerical coefficients and variables are raised to a power.

Multiplication of Like Bases

When multiplying expressions with the same base but different exponents, the exponents are added together. This property, often expressed as a^m * a^n = a^(m+n), streamlines the process of combining terms with identical bases during simplification.

Sign Considerations in Exponentiation

When dealing with negative bases raised to exponents, it is important to consider the parity of the exponent. An even exponent results in a positive outcome, while an odd exponent preserves the negative sign. This concept helps determine the correct sign of each term in an expression involving powers.

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