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

In mathematics, **scientific notation** is a way to express very large or very small numbers in a compact and convenient form. It follows the format:

**a x 10^b**

where 'a' is a number between 1 and 10, and 'b' is an integer representing the power of 10.

Let's simplify the expression **(5 x 10^3) x (9 x 10^7)** and express it in standard form.

**1. Multiply the coefficients:**

5 x 9 = 45

**2. Multiply the powers of 10:**

10^3 x 10^7 = 10^(3+7) = 10^10

**3. Combine the results:**

(5 x 10^3) x (9 x 10^7) = 45 x 10^10

**4. Adjust to standard form:**

Since 45 is greater than 10, we need to adjust the coefficient. We can rewrite 45 as 4.5 x 10^1. Now, we have:

4.5 x 10^1 x 10^10 = 4.5 x 10^(1+10) = **4.5 x 10^11**

Therefore, the product of (5 x 10^3) and (9 x 10^7) expressed in standard form is **4.5 x 10^11**.