%5E2-in-scientific-notation.jpeg "(3x10^3)^2 In Scientific Notation")
Simplifying (3 x 10^3)^2 in Scientific Notation
In mathematics, scientific notation is a way of expressing numbers that are very large or very small. It's especially helpful when dealing with powers of ten. Let's explore how to simplify the expression (3 x 10^3)^2 using scientific notation.
Understanding the Basics
- Scientific Notation: A number in scientific notation is written as a product of a number between 1 and 10 (inclusive) and a power of 10. For example, 2.5 x 10^6 is in scientific notation.
- Exponent Rules: When raising a power to another power, we multiply the exponents. For example, (x^m)^n = x^(m*n).
Simplifying the Expression
- Apply the exponent rule: (3 x 10^3)^2 = 3^2 x (10^3)^2
- Simplify the powers: 3^2 = 9 and (10^3)^2 = 10^(3*2) = 10^6
- Combine the results: 9 x 10^6
The Final Answer
Therefore, (3 x 10^3)^2 simplified in scientific notation is 9 x 10^6.