Question
Fully simplify using only positive exponents. \[ \frac{3 x^{8} y^{7}}{6 x^{6} y^{3}} \]
Ask by Mcfarlane Nichols. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\frac{x^{2} y^{4}}{2}
\]
Solution
To simplify the expression \(\frac{3 x^{8} y^{7}}{6 x^{6} y^{3}}\) using only positive exponents, follow these steps:
1. **Simplify the coefficients:**
\[
\frac{3}{6} = \frac{1}{2}
\]
2. **Simplify the \(x\)-terms:**
\[
\frac{x^{8}}{x^{6}} = x^{8-6} = x^{2}
\]
3. **Simplify the \(y\)-terms:**
\[
\frac{y^{7}}{y^{3}} = y^{7-3} = y^{4}
\]
4. **Combine the simplified parts:**
\[
\frac{1}{2} x^{2} y^{4} \quad \text{or} \quad \frac{x^{2} y^{4}}{2}
\]
Both forms are correct, but typically the expression is written with the constant in the denominator:
\[
\frac{x^{2} y^{4}}{2}
\]
**Final Answer:**
\[
\frac{x^{2} y^{4}}{2}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
Let's simplify the expression step by step. First, we can simplify the coefficients (the numerical part) and then the variables. The coefficients: \[ \frac{3}{6} = \frac{1}{2} \] Now for the variables \(x^8\) and \(x^6\): \[ \frac{x^{8}}{x^{6}} = x^{8-6} = x^{2} \] For the variables \(y^7\) and \(y^3\): \[ \frac{y^{7}}{y^{3}} = y^{7-3} = y^{4} \] Now, combine everything: \[ \frac{3 x^{8} y^{7}}{6 x^{6} y^{3}} = \frac{1}{2} x^{2} y^{4} \] Thus, the fully simplified expression using only positive exponents is: \[ \frac{1}{2} x^{2} y^{4} \]
