Rewrite the following expression with positive exponents.
$(24 x y)^{-\frac{3}{4}}$
Choose the correct equivalent expression.
A. $(24 x y)^{-\frac{3}{4}}=\frac{1}{(24 x y)^{\frac{4}{3}}}$
B. $(24 x y)^{-\frac{3}{4}}=\frac{1}{(24 x y)^{\frac{3}{4}}}$
C. $(24 x y)^{-\frac{3}{4}}=(24 x y)^{\frac{4}{3}}$
D. $(24 x y)^{-\frac{3}{4}}=-(24 x y)^{\frac{3}{4}}$
Answer (1)
Use the property of exponents a − n = a n 1 .
Apply the property to the expression: ( 24 x y ) − 4 3 = ( 24 x y ) 4 3 1 .
Identify the correct equivalent expression from the given options.
The final answer is ( 24 x y ) 4 3 1 .
Explanation
Understanding the problem We are given the expression ( 24 x y ) − 4 3 and we need to rewrite it using positive exponents.
Applying the exponent property Recall the property of exponents: a − n = a n 1 . Applying this property to the given expression, we get: ( 24 x y ) − 4 3 = ( 24 x y ) 4 3 1
Finding the correct option Now, we compare our result with the given options to find the correct equivalent expression.
Final Answer The correct equivalent expression is: ( 24 x y ) − 4 3 = ( 24 x y ) 4 3 1 which corresponds to option B.
Examples
Understanding how to manipulate exponents is crucial in various fields, such as physics and engineering. For example, when dealing with gravitational force, the force is inversely proportional to the square of the distance between two objects. If the distance is represented by d , the force can be expressed as F = k ⋅ d − 2 , where k is a constant. Rewriting this with positive exponents gives F = d 2 k , making it easier to understand and calculate the force at different distances.
