8 cubed in standard form and exponential form
The Correct Answer and Explanation is :
To find ( 8 ) cubed, we calculate ( 8^3 ).
Calculation
[
8^3 = 8 \times 8 \times 8
]
First, we multiply ( 8 \times 8 ):
[
8 \times 8 = 64
]
Next, we multiply ( 64 ) by ( 8 ):
[
64 \times 8 = 512
]
Thus, ( 8^3 = 512 ).
Standard Form and Exponential Form
- Standard Form: The result of ( 8^3 ) in standard form is ( 512 ).
- Exponential Form: The exponential form remains ( 8^3 ).
Explanation
Exponential notation is a mathematical way to express repeated multiplication. The base number, ( 8 ) in this case, is multiplied by itself a specified number of times, denoted by the exponent, which is ( 3 ). This notation allows for easier representation of large numbers and simplifies calculations.
When we calculate ( 8^3 ), we are expressing that we take the number ( 8 ) and multiply it by itself twice more (for a total of three times). This is useful in various applications, such as calculating volumes in geometry, where cubing is relevant when dealing with three-dimensional objects.
In practical scenarios, cubing is important in fields like engineering, physics, and computer science, where volume calculations or growth rates might be required. For instance, if one were to determine the volume of a cube with side length ( 8 ), the volume would be calculated as ( V = s^3 = 8^3 ), leading to ( 512 ) cubic units.
Understanding both the standard and exponential forms helps bridge conceptual gaps in mathematics, especially in advanced topics involving polynomial expressions, exponential growth, and logarithmic functions. Thus, recognizing how to manipulate these forms is crucial for further mathematical learning and real-world problem-solving.