7 to the power of 2 in expanded form
The Correct Answer and Explanation is :
The correct answer is: 49
To express (7) to the power of (2) in expanded form, we can write it as:
[
7^2 = 7 \times 7
]
Now, let’s calculate the value:
[
7 \times 7 = 49
]
Thus, (7^2) equals (49).
Explanation of Exponents
Exponents, or powers, are a way to represent repeated multiplication of a number by itself. The expression (a^n) indicates that the number (a) is multiplied by itself (n) times. In the case of (7^2), the base is (7) and the exponent is (2), meaning we multiply (7) by itself two times.
Expanded Form:
The expanded form of (7^2) is simply written as (7 \times 7). This notation is useful for understanding the concept of exponents, especially for beginners. It visually illustrates how many times the base is being multiplied.
Calculating Exponents:
When calculating (7^2), we perform the multiplication as follows:
- Start with the base: (7).
- Multiply (7) by itself:
[
7 \times 7
] - Calculate the result:
[
7 \times 7 = 49
]
Applications of Exponents:
Understanding exponents is essential not only in mathematics but also in various fields such as physics, engineering, and computer science. They simplify expressions, making calculations easier, especially with large numbers. For example, instead of writing (7) multiplied by itself (2) times, we can simply use (7^2), which is more concise.
Conclusion:
In summary, (7^2) in expanded form is (7 \times 7), which equals (49). Mastering the concept of exponents allows for more efficient calculations and deeper comprehension of mathematical principles.