The power of a quotient rule states that the power of a quotient is equal to the power of each term in the numerator and denominator raised individually.
Understanding the Power of a Quotient Rule
The power of a quotient rule is a fundamental concept in algebra that simplifies expressions involving fractions raised to a power. Essentially, it allows you to distribute the exponent to both the numerator and the denominator of the fraction.
Formula
The formula representing the power of a quotient rule is:
(a/b)^m = (a^m)/(b^m)
Where:
- a and b are any real numbers (with b ≠ 0).
- m is any integer exponent.
This means that raising a fraction (a/b) to the power of m is the same as raising both the numerator (a) and the denominator (b) to the power of m separately, and then dividing the result.
Examples
Here are some examples to illustrate the power of a quotient rule:
- (2/3)^2 = (2^2)/(3^2) = 4/9
- (x/y)^3 = (x^3)/(y^3)
- (4/z)^5 = (4^5)/(z^5) = 1024/(z^5)
Key Takeaways
- The exponent outside the parentheses is distributed to both the numerator and the denominator.
- This rule only applies when the entire quotient is raised to a power.
- Understanding this rule simplifies complex algebraic expressions.
