According to the power of a quotient, how should you handle the numerator and denominator?

According to the power of a quotient, how should you handle the numerator and denominator?

• A. Find the power of the numerator and the power of the denominator separately
• B. Combine the powers of numerator and denominator
• C. Only consider the denominator
• D. Ignore the powers

Answer: (A)

When applying the power of a quotient rule, the correct approach is to find the power of the numerator and the power of the denominator separately. This rule is expressed mathematically as \((\frac{a}{b})^n = \frac{a^n}{b^n}\), meaning that when you raise a fraction to a power, you can distribute that power to both the numerator and the denominator independently. By taking this approach, you ensure that each part of the fraction is raised correctly to the power indicated. Thus, if you have a fraction like \((\frac{x^2}{y^3})^3\), you would calculate it as \(\frac{(x^2)^3}{(y^3)^3}\), which simplifies to \(\frac{x^6}{y^9}\). This rule is fundamental in simplifying expressions containing exponents and allows for clearer calculations in more complex algebraic expressions.

When applying the power of a quotient rule, the correct approach is to find the power of the numerator and the power of the denominator separately. This rule is expressed mathematically as ((\frac{a}{b})^n = \frac{a^n}{b^n}), meaning that when you raise a fraction to a power, you can distribute that power to both the numerator and the denominator independently.

By taking this approach, you ensure that each part of the fraction is raised correctly to the power indicated. Thus, if you have a fraction like ((\frac{x^2}{y^3})^3), you would calculate it as (\frac{(x^2)^3}{(y^3)^3}), which simplifies to (\frac{x^6}{y^9}). This rule is fundamental in simplifying expressions containing exponents and allows for clearer calculations in more complex algebraic expressions.