Which is equal to $(11-6)^3$?
A. 85
B. 1,115
C. 125
D. 15
Answer (1)
Evaluate the expression inside the parentheses: 11 − 6 = 5 .
Raise the result to the power of 3: 5 3 = 5 × 5 × 5 = 125 .
Compare the result with the given options and choose the correct one.
The final answer is 125 .
Explanation
Understanding the Problem We are asked to evaluate the expression ( 11 − 6 ) 3 and determine which of the given options is equal to it.
Evaluating Parentheses First, we need to evaluate the expression inside the parentheses: 11 − 6 = 5 .
Calculating the Power Next, we raise the result to the power of 3: 5 3 = 5 × 5 × 5 = 125 .
Finding the Correct Answer Finally, we compare the result with the given options: 85, 1115, 125, and 15. The correct answer is 125.
Examples
Understanding exponents is crucial in many real-world scenarios, such as calculating compound interest. For instance, if you invest 100 a t anann u a l in t eres t r a t eo f 5 A = P(1 + r)^t , w h ere A i s t h e f ina l am o u n t , P$ is the principal amount ( 100 ) , r i s t h e in t eres t r a t e ( 0.05 ) , an d t i s t h e n u mb ero f ye a rs ( 3 ) . S o , A = 100(1 + 0.05)^3 = 100(1.05)^3 = 100 \times 1.157625 = $115.76. This demonstrates how exponents help us understand growth and change over time.
