%5E2.jpeg "(3x10^3)^2")
Understanding (3x10^3)^2
This expression represents the square of a number written in scientific notation. Let's break it down step-by-step:
Scientific Notation
- 3 x 10^3 is the scientific notation of the number 3000. It's a way to express large numbers more compactly.
- 3 is the coefficient, representing the significant digits.
- 10^3 is the base-10 exponential term, indicating the magnitude of the number (10 raised to the power of 3 equals 1000).
Squaring the Expression
When we square (3 x 10^3)^2, we are multiplying the entire expression by itself:
(3 x 10^3)^2 = (3 x 10^3) * (3 x 10^3)
Applying the Laws of Exponents
To simplify this, we apply the laws of exponents:
- (a * b)^n = a^n * b^n
- (a^m)^n = a^(m*n)
Applying these rules to our expression:
(3 x 10^3)^2 = 3^2 * (10^3)^2
Calculating the Result
- 3^2 = 9
- (10^3)^2 = 10^(3*2) = 10^6
Therefore, (3 x 10^3)^2 = 9 x 10^6
Conclusion
In conclusion, (3 x 10^3)^2 is equivalent to 9 x 10^6, which is the scientific notation for 9,000,000.