12x12x12x12
The Correct Answer and Explanation is:
The expression ( 12 \times 12 \times 12 \times 12 ) equals 20,736.
Explanation:
The expression ( 12 \times 12 \times 12 \times 12 ) involves multiplying the number 12 by itself four times. This is equivalent to raising 12 to the power of 4, or ( 12^4 ).
- Step-by-Step Calculation:
- First, calculate ( 12 \times 12 ):
[
12 \times 12 = 144
] - Next, take this result and multiply it by 12 again:
[
144 \times 12 = 1,728
] - Finally, multiply the result by 12 one more time:
[
1,728 \times 12 = 20,736
]
- Using Exponents:
When a number is multiplied by itself multiple times, it’s often more concise to use exponents. Here, ( 12 \times 12 \times 12 \times 12 ) can be rewritten as ( 12^4 ), meaning “12 raised to the power of 4.” - Exponential Growth:
This expression demonstrates the concept of exponential growth. Each multiplication by 12 significantly increases the value. For instance:
- ( 12^1 = 12 )
- ( 12^2 = 144 )
- ( 12^3 = 1,728 )
- ( 12^4 = 20,736 ) As seen, each additional multiplication by 12 has a large impact on the final result.
- Practical Applications:
Such calculations are useful in various contexts, like volume measurement. If a cube has a side length of 12 units, then its volume (which is calculated as side length cubed, or ( s^3 )) would be ( 12 \times 12 \times 12 = 1,728 ) cubic units. However, if considering a 4-dimensional space (hypothetically), this calculation might represent the “4-dimensional volume” of a hypercube.
In summary, multiplying 12 by itself four times yields a substantial result due to exponential growth, resulting in 20,736.