Question
(1) How many factors of 10 are in the quotient? Number of factors of 10 in \( \frac{10^{6}}{10^{4}} \) :
Ask by Pierce Carroll. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
There are 2 factors of 10 in the quotient.
Solution
We start with the expression:
(10^6) / (10^4).
Using the rule of exponents for division (subtract the exponents), we have:
10^(6−4) = 10^2.
This means that the quotient has 10 as a factor exactly 2 times, i.e., it is 10 * 10 = 100.
So, there are 2 factors of 10 in the quotient.
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Simplify this solution The Deep Dive
When you divide \(10^{6}\) by \(10^{4}\), you subtract the exponents: \(6 - 4 = 2\). Therefore, the quotient is \(10^{2}\), which means there are 2 factors of 10 in the result! So, the answer is simply 2. It's like making a super simple recipe! When you have 6 bananas and you take away 4, how many do you have left to make a delicious banana smoothie? You’ve got 2 bananas, and the same goes for our factors of 10!
