Rewrite 3x3x3x3x3 using an exponent
The Correct Answer and Explanation is :
The correct answer is: (3^5)
The expression (3 \times 3 \times 3 \times 3 \times 3) can be rewritten using an exponent as (3^5).
Explanation:
The notation (a^n) is used to denote exponentiation, where (a) is the base, and (n) is the exponent. The exponent tells you how many times to multiply the base by itself. In this case, (3) is the base, and the exponent (5) indicates that (3) is multiplied by itself a total of five times.
To understand how this works, let’s break it down step by step:
- Definition of Exponentiation: Exponentiation is a mathematical operation involving two numbers, the base and the exponent. For instance, (a^n) means multiplying (a) by itself (n) times. So, (a^3 = a \times a \times a).
- Applying to the Current Problem: Here, we have (3) being multiplied by itself five times:
[
3 \times 3 \times 3 \times 3 \times 3 = 3^5
]
This indicates that we are dealing with five instances of the number three. - Calculating the Value: To find the actual value of (3^5), we can perform the multiplication:
- First, calculate (3 \times 3 = 9).
- Next, multiply (9) by (3) to get (27).
- Then, multiply (27) by (3) to get (81).
- Finally, multiply (81) by (3) to arrive at (243).
Thus, (3^5 = 243).
- Properties of Exponents: This property of expressing repeated multiplication using exponents simplifies calculations and notation, especially for larger numbers. It also leads to a deeper understanding of powers and their relationships, allowing for efficient problem-solving in algebra and other mathematical fields.
In conclusion, (3 \times 3 \times 3 \times 3 \times 3) can be expressed as (3^5), and it evaluates to (243). This notation not only simplifies expressions but also plays a crucial role in advanced mathematical concepts, making it essential for both basic and higher-level mathematics.