Simplify: $14^3+1.4^2+2.9^0$
A. $2,746.96$
B. $2,748.3$
C. $2,747.9$
D. $2,748.86$
Answer (2)
Calculate 1 4 3 = 2744 .
Calculate 1. 4 2 = 1.96 .
Calculate 2. 9 0 = 1 .
Add the results: 2744 + 1.96 + 1 = 2746.96 .
Explanation
Understanding the Expression We need to simplify the expression 1 4 3 + 1. 4 2 + 2. 9 0 . This involves calculating each term separately and then adding them together. Let's start by evaluating each term.
Calculating 14 cubed First, we calculate 1 4 3 , which means 14 × 14 × 14 . The result is 2744.
Calculating 1.4 squared Next, we calculate 1. 4 2 , which means 1.4 × 1.4 . The result is 1.96.
Calculating 2.9 to the power of 0 Then, we calculate 2. 9 0 . Any non-zero number raised to the power of 0 is 1. So, 2. 9 0 = 1 .
Adding the Results Finally, we add the results together: 2744 + 1.96 + 1 = 2746.96 .
Final Answer Therefore, the simplified expression is 2746.96 .
Examples
Imagine you are calculating the total cost of materials for a project. You need 14 cubic meters of concrete at a base cost, plus a small area of special coating (1.4 square meters), and a fixed activation fee. This problem is similar to calculating the total cost: 1 4 3 represents the base cost, 1. 4 2 represents the coating cost, and 2. 9 0 represents the activation fee. Adding these together gives the total project cost. This type of calculation is useful in various fields, such as construction, engineering, and finance, where you need to combine different quantities with varying units or scales.
The expression 1 4 3 + 1. 4 2 + 2. 9 0 simplifies to 2746.96 after calculating each term and adding them together. The correct answer is option A.
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