Answer:
20 times.
Skills needed: Cancelling out Like Terms, Division
Step-by-step explanation:
1) To find out "many times as large as" a number is, we utilize division.
- Example: 8 is how many times as large as 4. [tex]8 \div 4=2[/tex], 2 times.
2) Therefore we can divide the 1st expression by the 2nd expression
This is what we need to solve: [tex]\frac{8*10^3}{4*10^2}[/tex]
Let's break it down into two parts: The left part, which is [tex]\frac{8}{4}[/tex], and the right part, which would be [tex]\frac{10^3}{10^2}[/tex].
The left part is really easy to solve out: [tex]\frac{8}{4} = 8 \div 4 = 2[/tex]
3) The harder right part:
Now, we can evaluate [tex]10^3[/tex] to be 1000, and [tex]10^2[/tex] to be 100, and then divide, but that is not the most efficient method.
Let's use an exponent rule:
[tex]\frac{a^b}{a^c}=a^{b-c}[/tex]
- Example: [tex]\frac{4^4}{4^2}=4^{4-2}=4^2=16[/tex]
Let's use that for [tex]\frac{10^3}{10^2}[/tex]
---> [tex]\frac{10^3}{10^2} = 10^{3-2} = 10^1=10[/tex]
Therefore, the right part equals 10.
4) The final product is [tex]\text{left part} * \text{right part}[/tex] = [tex]2*10=20[/tex]
Therefore, 20 is the answer.
================================================================== Hope you understood, and have a nice day!
