(((a b^2 c)^-3)/(b^-3))^2

Name: Problem 57, Chapter 1: Algebra and Trigonometry
Uploaded: 2020-07-10T18:49:40-08:00
Duration: 1 min 54 s
Channel: Joseph Lentino
Description: (((a b^2 c)^-3)/(b^-3))^2

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Key Concepts

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the corresponding positive exponent. For example, a^(-n) is equivalent to 1/(a^n). This concept helps simplify expressions where terms have negative powers by converting them into fractions.

Power of a Product

The power of a product rule states that when a product of factors is raised to an exponent, each factor is raised to that exponent separately. Mathematically, (abc)^n equals a^n * b^n * c^n, which is useful for distributing the exponent across multiple variables.

Power of a Power

The power of a power rule is used when an exponent is applied to an expression that is already raised to an exponent. The exponents multiply in such cases, so (a^m)^n equals a^(m*n). This rule simplifies repeated exponentiation of the same base.

Division Rule for Exponents

The division rule for exponents states that when dividing two expressions with the same base, you subtract the exponent in the denominator from the exponent in the numerator. That is, a^m / a^n equals a^(m-n). This principle is crucial for simplifying expressions that involve fractional exponents or the division of powers.

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