%5E-2-in-scientific-notation.jpeg "(5x10^-10)^-2 In Scientific Notation")
Simplifying (5 x 10^-10)^-2 in Scientific Notation
This problem involves simplifying an expression with negative exponents and scientific notation. Here's how to break it down:
Understanding the Rules
- Negative Exponent: A negative exponent means you take the reciprocal of the base raised to the positive version of that exponent. For example, x^-2 = 1/x^2.
- Power of a Product: When raising a product to a power, you raise each factor to that power. For example, (xy)^n = x^n * y^n.
- Power of a Power: When raising a power to another power, you multiply the exponents. For example, (x^m)^n = x^(m*n).
Applying the Rules
- Reciprocal: (5 x 10^-10)^-2 is the same as 1 / (5 x 10^-10)^2
- Power of a Product: 1 / (5 x 10^-10)^2 = 1 / (5^2 * (10^-10)^2)
- Power of a Power: 1 / (5^2 * (10^-10)^2) = 1 / (25 * 10^-20)
Simplifying and Scientific Notation
- Calculate: 1 / (25 * 10^-20) = 0.04 * 10^20
- Scientific Notation: To express the result in proper scientific notation, we need a number between 1 and 10 multiplied by a power of 10. Moving the decimal place two places to the right, we get 4 * 10^18.
Final Answer
Therefore, (5 x 10^-10)^-2 simplified in scientific notation is 4 x 10^18.