Write the following expression using exponents.
4x4x4x4 =
The Correct Answer and Explanation is:
The expression (4 \times 4 \times 4 \times 4) can be rewritten using exponents as (4^4).
Explanation
Understanding Exponents:
Exponents are a shorthand way to represent repeated multiplication of the same number. In the expression (a^n), (a) is called the base, and (n) is called the exponent. The exponent indicates how many times the base is multiplied by itself. For example, (a^3) means (a \times a \times a).
Applying Exponents to the Expression:
In the case of the expression (4 \times 4 \times 4 \times 4), the base is 4, and it is being multiplied by itself a total of four times. Hence, we can express this as (4^4). This notation conveys the same mathematical meaning while simplifying the expression.
Calculating the Value:
To further understand the value of (4^4), we can compute it:
[
4^4 = 4 \times 4 \times 4 \times 4
]
Calculating step by step:
- First, multiply the first two 4s:
[
4 \times 4 = 16
] - Next, take that result and multiply by the next 4:
[
16 \times 4 = 64
] - Finally, multiply this result by the last 4:
[
64 \times 4 = 256
]
Thus, (4^4) not only simplifies the expression but also leads us to the numerical result of 256.
Why Use Exponents?
Using exponents simplifies the representation of mathematical expressions, making them easier to read and understand, especially when dealing with larger numbers or more complex equations. This simplification is particularly useful in algebra and higher-level mathematics, where compact notation can significantly enhance clarity and efficiency in calculations.
In summary, the expression (4 \times 4 \times 4 \times 4) can be concisely expressed as (4^4), which not only streamlines the representation but also allows for easier computation and interpretation of the underlying mathematical concept.