Question
Simplify the following expression. Write the result using positive exponents only. Assume t \( \frac{-18 a^{6} b}{9 a b^{7}} \)
Ask by Hilton Little. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\(\frac{-2a^{5}}{b^{6}}\)
Solution
To simplify the expression \(\frac{-18 a^{6} b}{9 a b^{7}}\) and write it using positive exponents only, follow these steps:
1. **Simplify the coefficients:**
\[
\frac{-18}{9} = -2
\]
2. **Simplify the \(a\) terms:**
\[
\frac{a^6}{a} = a^{6-1} = a^5
\]
3. **Simplify the \(b\) terms:**
\[
\frac{b}{b^7} = b^{1-7} = b^{-6} = \frac{1}{b^6}
\]
4. **Combine the results:**
\[
-2 \cdot a^5 \cdot \frac{1}{b^6} = \frac{-2a^5}{b^6}
\]
Therefore, the simplified expression with positive exponents is:
\[
\boxed{\dfrac{-2a^{5}}{b^{6}}}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To simplify the expression \(\frac{-18 a^{6} b}{9 a b^{7}}\), start by dividing the coefficients: \(-18 \div 9 = -2\). Next, simplify the variables. For \(a\), \(a^{6} \div a = a^{6-1} = a^{5}\). For \(b\), \(b \div b^{7} = b^{1-7} = b^{-6}\). Combining these, we get \(-2 a^{5} b^{-6}\). Now, to express this with positive exponents only, rewrite \(b^{-6}\) as \(\frac{1}{b^{6}}\). Therefore, the final simplified expression is: \(-\frac{2 a^{5}}{b^{6}}\).
