Explore IDNLearn.com's extensive Q&A database and find the answers you need. Get accurate and comprehensive answers from our network of experienced professionals.
Sagot :
To solve the given expression
[tex]\[ \frac{\left(4 m^2 n\right)^2}{2 m^5 n}, \][/tex]
we need to simplify it step by step.
### Step 1: Simplify the numerator
First, let's simplify the numerator [tex]\((4 m^2 n)^2\)[/tex].
[tex]\[ (4 m^2 n)^2 = 4^2 \cdot (m^2)^2 \cdot n^2 = 16 \cdot m^4 \cdot n^2 \][/tex]
Thus, the numerator simplifies to [tex]\( 16 m^4 n^2 \)[/tex].
### Step 2: Rewrite the expression with the simplified numerator
Now, substitute the simplified numerator back into the expression:
[tex]\[ \frac{16 m^4 n^2}{2 m^5 n} \][/tex]
### Step 3: Simplify the expression
Next, we need to divide the numerator by the denominator. Let's break it down:
[tex]\[ \frac{16 m^4 n^2}{2 m^5 n} = \frac{16}{2} \cdot \frac{m^4}{m^5} \cdot \frac{n^2}{n} \][/tex]
Simplify each part separately:
- [tex]\(\frac{16}{2} = 8\)[/tex]
- [tex]\(\frac{m^4}{m^5} = m^{4-5} = m^{-1}\)[/tex]
- [tex]\(\frac{n^2}{n} = n^{2-1} = n\)[/tex]
### Step 4: Combine the simplified components
Putting it all together:
[tex]\[ 8 \cdot m^{-1} \cdot n = 8 m^{-1} n \][/tex]
### Conclusion
The equivalent expression is [tex]\(8 m^{-1} n\)[/tex], which corresponds to option B.
So, the correct answer is:
[tex]\[ \boxed{B. \, 8 m^{-1} n} \][/tex]
[tex]\[ \frac{\left(4 m^2 n\right)^2}{2 m^5 n}, \][/tex]
we need to simplify it step by step.
### Step 1: Simplify the numerator
First, let's simplify the numerator [tex]\((4 m^2 n)^2\)[/tex].
[tex]\[ (4 m^2 n)^2 = 4^2 \cdot (m^2)^2 \cdot n^2 = 16 \cdot m^4 \cdot n^2 \][/tex]
Thus, the numerator simplifies to [tex]\( 16 m^4 n^2 \)[/tex].
### Step 2: Rewrite the expression with the simplified numerator
Now, substitute the simplified numerator back into the expression:
[tex]\[ \frac{16 m^4 n^2}{2 m^5 n} \][/tex]
### Step 3: Simplify the expression
Next, we need to divide the numerator by the denominator. Let's break it down:
[tex]\[ \frac{16 m^4 n^2}{2 m^5 n} = \frac{16}{2} \cdot \frac{m^4}{m^5} \cdot \frac{n^2}{n} \][/tex]
Simplify each part separately:
- [tex]\(\frac{16}{2} = 8\)[/tex]
- [tex]\(\frac{m^4}{m^5} = m^{4-5} = m^{-1}\)[/tex]
- [tex]\(\frac{n^2}{n} = n^{2-1} = n\)[/tex]
### Step 4: Combine the simplified components
Putting it all together:
[tex]\[ 8 \cdot m^{-1} \cdot n = 8 m^{-1} n \][/tex]
### Conclusion
The equivalent expression is [tex]\(8 m^{-1} n\)[/tex], which corresponds to option B.
So, the correct answer is:
[tex]\[ \boxed{B. \, 8 m^{-1} n} \][/tex]
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Thank you for choosing IDNLearn.com. We’re here to provide reliable answers, so please visit us again for more solutions.