What expression is equivalent to 3 to the 5th power?
The Correct Answer and Explanation is:
The expression that is equivalent to ( 3^5 ) is:
[
3^5 = 3 \times 3 \times 3 \times 3 \times 3
]
Explanation:
The notation ( 3^5 ) is an example of an exponentiation, where 3 is the base and 5 is the exponent (or power). This expression indicates that 3 should be multiplied by itself a total of 5 times. In mathematical terms:
[
3^5 = 3 \times 3 \times 3 \times 3 \times 3
]
This process of multiplying a number by itself multiple times is called repeated multiplication. Each time we multiply 3 by itself, we are increasing the power or exponent by one.
Step-by-Step Breakdown:
- Start with the base number ( 3 ).
- Multiply ( 3 \times 3 = 9 ).
- Multiply ( 9 \times 3 = 27 ).
- Multiply ( 27 \times 3 = 81 ).
- Finally, multiply ( 81 \times 3 = 243 ).
Thus, ( 3^5 = 243 ).
Key Concepts:
- Base: The number that is being multiplied, which is 3 in this case.
- Exponent: The number that tells you how many times to multiply the base by itself. Here, the exponent is 5.
- Exponentiation: This is a shorthand for repeated multiplication. Instead of writing out the long multiplication process, we can express it with a base and an exponent. For example, ( 3^5 ) is more efficient than writing out ( 3 \times 3 \times 3 \times 3 \times 3 ).
Exponentiation is a powerful tool in mathematics, especially for dealing with large numbers. It is also a foundational concept in algebra, number theory, and calculus, making it an essential skill to master.
Thus, the expression ( 3^5 ) simplifies to 243.