Question
Simplify. \[ \frac{4 m^{-8} n^{9}}{16 n^{-4} m^{-7}} \]
Ask by Hodgson Luna. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified form is \( \frac{n^{13}}{4m} \).
Solution
Calculate or simplify the expression \( \frac{4m^{-8}n^{9}}{16n^{-4}m^{-7}} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{4m^{-8}n^{9}}{16n^{-4}m^{-7}}\)
- step1: Multiply by \(a^{-n}:\)
\(\frac{4m^{-8}n^{9}m^{7}n^{4}}{16}\)
- step2: Multiply:
\(\frac{4m^{-1}n^{13}}{16}\)
- step3: Reduce the fraction:
\(\frac{m^{-1}n^{13}}{4}\)
- step4: Rewrite the expression:
\(\frac{\frac{n^{13}}{m}}{4}\)
- step5: Simplify:
\(\frac{n^{13}}{4m}\)
The simplified form of the expression \(\frac{4m^{-8}n^{9}}{16n^{-4}m^{-7}}\) is \(\frac{n^{13}}{4m}\).
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Simplify this solution The Deep Dive
To simplify the expression \[ \frac{4 m^{-8} n^{9}}{16 n^{-4} m^{-7}}, \] we start by dividing the coefficients and the variables separately. 1. **Coefficients**: \[ \frac{4}{16} = \frac{1}{4}. \] 2. **For \(m\)**: \[ \frac{m^{-8}}{m^{-7}} = m^{-8 - (-7)} = m^{-8 + 7} = m^{-1} = \frac{1}{m}. \] 3. **For \(n\)**: \[ \frac{n^{9}}{n^{-4}} = n^{9 - (-4)} = n^{9 + 4} = n^{13}. \] Putting it all together, we have: \[ \frac{4 m^{-8} n^{9}}{16 n^{-4} m^{-7}} = \frac{1}{4} \cdot \frac{n^{13}}{m} = \frac{n^{13}}{4m}. \] Thus, the simplified form is \[ \boxed{\frac{n^{13}}{4m}}. \]
