Question
Fully simplify using only positive exponents. \[ \frac{2 x^{7} y^{3}}{x^{6} y^{5}} \]
Ask by Gough Willis. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\frac{2x}{y^{2}}
\]
Solution
To simplify the expression \(\frac{2 x^{7} y^{3}}{x^{6} y^{5}}\) with only positive exponents, follow these steps:
1. **Simplify the exponents for \(x\) and \(y\):**
\[
\frac{x^{7}}{x^{6}} = x^{7-6} = x^{1} = x
\]
\[
\frac{y^{3}}{y^{5}} = y^{3-5} = y^{-2}
\]
2. **Combine the simplified terms:**
\[
2 \cdot x \cdot y^{-2}
\]
3. **Rewrite using only positive exponents by moving \(y^{-2}\) to the denominator:**
\[
\frac{2x}{y^{2}}
\]
So, the fully simplified expression with only positive exponents is:
\[
\frac{2x}{y^{2}}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To simplify the expression \(\frac{2 x^{7} y^{3}}{x^{6} y^{5}}\), we begin by dividing the coefficients and then the powers of the variables separately. 1. Dividing the coefficients: \[ \frac{2}{1} = 2 \] 2. Dividing the powers of \(x\): \[ x^{7} \div x^{6} = x^{7-6} = x^{1} = x \] 3. Dividing the powers of \(y\): \[ y^{3} \div y^{5} = y^{3-5} = y^{-2} \] Since we only want positive exponents, we rewrite \(y^{-2}\) as \(\frac{1}{y^{2}}\). Now putting it all together: \[ \frac{2 x^{1} y^{3}}{x^{6} y^{5}} = 2 x \cdot \frac{1}{y^{2}} = \frac{2x}{y^{2}} \] Thus, the fully simplified expression is: \[ \frac{2x}{y^{2}} \]
