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When multiplying numbers with exponents, it's important to understand and apply the rules of exponents. The primary rule used in our exercise is the product of powers rule. This rule states that you simply add the exponents when multiplying two numbers with the same base. For example, if you have \(10^a \times 10^b\), the product will be \(10^{a + b}\).
In the provided exercise, you multiply \(10^8 \times 10^{-5}\). According to the rule, you add the exponents 8 and -5, which gives you 3. Thus, the result is \(10^3\).
Make sure whenever you encounter exponent multiplication, to check that the bases are the same and apply this straightforward rule.

Simplifying expressions involves reducing them to their simplest form. In our example, we simplified the expression \( (2.4 \times 10^8)(2 \times 10^{-5}) \). Here's how we did it:

• First, multiply the coefficients: \(2.4 \times 2 = 4.8\)
• Next, add the exponents: \( 8 + (-5) = 3 \)
• Finally, combine the coefficients and exponents: \( 4.8 \times 10^3 \)

Simplifying expressions can make complex calculations more manageable and can help you see the relationships between different parts of the equation.

Pre-algebra is the foundational math that prepares you for algebra. It covers basic operations with numbers, including addition, subtraction, multiplication, and division, along with the basic rules for working with exponents and expressions. The exercise we worked on is a classic example from pre-algebra.
Here we dealt with multiplication, understanding exponents, and combining numbers in a simplified form. Pre-algebra also introduces you to the properties of numbers and how they interact with each other. By mastering pre-algebra, you build a strong base that will make learning algebra and more advanced math topics easier.
Make sure to practice various problems, focusing on understanding each step, as these skills are crucial for your future math endeavors.