Which law would you use to simplify the expression $\left(\frac{p}{q}\right)^3$?
A. power of a power
B. power of a quotient
C. quotient of powers
D. power of a product
Answer (1)
The power of a quotient rule states that ( b a ) n = b n a n . Applying this rule to the expression ( q p ) 3 results in q 3 p 3 . Therefore, the correct answer is power of a quotient.
Explanation
Understanding the Problem We are asked to identify the law of exponents that simplifies the expression ( q p ) 3 . Let's analyze the options.
Recalling the Power of a Quotient Rule The power of a quotient rule states that when you have a quotient raised to a power, you distribute the power to both the numerator and the denominator. In other words: ( b a ) n = b n a n
Applying the Rule Applying this rule to our expression, we get: ( q p ) 3 = q 3 p 3 This simplifies the given expression.
Conclusion Therefore, the law we use to simplify the expression ( q p ) 3 is the power of a quotient.
Examples
The power of a quotient rule is useful in various real-world scenarios. For instance, if you are scaling a recipe that involves ratios, such as tripling a recipe that calls for 2 1 cup of flour, you effectively apply this rule. The new amount of flour would be ( 2 1 ) × 3 = 2 3 1 3 = 2 3 cups. This concept extends to scaling maps, architectural designs, and engineering models where maintaining proportions is crucial.
