3 x 5 to the power of 2
The Correct Answer and Explanation is :
To solve (3 \times 5^2), we follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
- Calculate the exponent: Start with (5^2).
[
5^2 = 5 \times 5 = 25
] - Multiply the result by 3: Now, we multiply this result by 3.
[
3 \times 25 = 75
]
So, the final answer to (3 \times 5^2) is (75).
Explanation:
The expression (3 \times 5^2) involves a multiplication operation and an exponentiation operation. Exponentiation is performed first because it takes precedence over multiplication in the order of operations.
When we see (5^2), it means we multiply 5 by itself. This concept of exponentiation is fundamental in mathematics, representing repeated multiplication. In this case, (5) is the base, and (2) is the exponent, indicating that the base should be multiplied by itself two times.
After calculating (5^2) and obtaining (25), we then perform the multiplication. The multiplication operation, represented by the symbol (\times), combines quantities together. Here, multiplying (3) by (25) gives us the total, which is (75).
This step-by-step approach ensures accuracy and clarity in mathematical calculations. Understanding the order of operations is crucial in solving more complex mathematical expressions correctly. By adhering to these rules, we can tackle increasingly intricate equations without confusion. Thus, our final result of (75) demonstrates both the power of exponents and the importance of following mathematical conventions.