## Simplifying Scientific Notation: (5 x 10^3) x (9 x 10^7)

This expression involves multiplying two numbers written in scientific notation. To simplify this, we need to understand the properties of exponents.

### Understanding the Properties of Exponents

**Multiplying exponents with the same base:**When multiplying exponents with the same base, we add the powers. For example, x^m * x^n = x^(m+n).**Multiplying numbers in scientific notation:**We multiply the coefficients and add the exponents of the powers of 10.

### Simplifying the Expression

**Multiply the coefficients:**5 x 9 = 45**Add the exponents of 10:**10^3 x 10^7 = 10^(3+7) = 10^10

### The Result

Therefore, (5 x 10^3) x (9 x 10^7) = **45 x 10^10**.

This can be expressed in standard scientific notation as **4.5 x 10^11**.