%5E3.jpeg "(2x10^-3)^3")
Understanding (2 x 10^-3)^3
This expression involves two key mathematical concepts: exponents and scientific notation. Let's break it down step by step.
Understanding Exponents
An exponent indicates how many times a base number is multiplied by itself. For example, 2^3 means 2 multiplied by itself three times: 2 x 2 x 2 = 8.
Understanding Scientific Notation
Scientific notation is a way of expressing very large or very small numbers concisely. It uses the form a x 10^b, where 'a' is a number between 1 and 10, and 'b' is an integer. For example, 2 x 10^-3 represents 0.002.
Solving (2 x 10^-3)^3
To solve this expression, we need to apply the exponent to both the coefficient (2) and the power of 10.
- Step 1: Cube the coefficient. (2)^3 = 2 x 2 x 2 = 8
- Step 2: Cube the power of 10. (10^-3)^3 = 10^(-3 x 3) = 10^-9
Now, we combine the results:
8 x 10^-9
Simplifying the Answer
This answer is already in scientific notation. However, we can express it in standard form: 0.000000008
Conclusion
The expression (2 x 10^-3)^3 is equal to 8 x 10^-9, which is equivalent to 0.000000008. This example demonstrates how to apply exponents and scientific notation effectively in mathematical calculations.