Which is equivalent to $(60-30)^3$?
A. 900
B. 2,700
C. 27,000
Answer (2)
Simplify the expression inside the parentheses: 60 − 30 = 30 .
Calculate the cube: 3 0 3 = 30 × 30 × 30 .
Perform the multiplication: 30 × 30 × 30 = 27000 .
The equivalent value is 27 , 000 .
Explanation
Simplify the Parentheses First, we need to simplify the expression inside the parentheses. We have 60 − 30 = 30 .
Calculate the Cube Next, we need to calculate the cube of the result from the previous step. That is, we need to calculate 3 0 3 , which means 30 × 30 × 30 .
Perform the Multiplication Now, let's calculate 30 × 30 × 30 . We know that 30 × 30 = 900 . Then, we multiply 900 × 30 = 27000 .
Identify the Correct Option Finally, we compare our calculated value, 27000, with the given options. Option A is 900, Option B is 2,700, and Option C is 27,000. The correct option is C, which matches our calculated value.
Examples
Understanding exponents is crucial in many real-world scenarios, such as calculating compound interest. For example, if you invest 1000 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 ( 1000 ) , 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 = 1000(1 + 0.05)^3 = 1000(1.05)^3 = 1000 \times 1.157625 = $1157.63. This shows how exponents help in understanding growth and accumulation over time.
The value of ( 60 − 30 ) 3 is 27,000, which matches option C. This was determined by simplifying the expression to 30 and then calculating 3 0 3 , which equals 27,000. Therefore, the correct answer is C.
;
