Question
Simplify. \[ \frac{z^{3} y^{5} a^{6}}{z^{4} y} \] \( \square \)
Ask by Harmon Donnelly. in the United States
Jan 29,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\[
\frac{y^{4}a^{6}}{z}
\]
Solution
To simplify the expression:
\[
\frac{z^{3} y^{5} a^{6}}{z^{4} y}
\]
Follow these steps:
1. **Apply the Quotient Rule for Exponents:** Subtract the exponents of like bases in the numerator and the denominator.
- For \( z \):
\[
z^{3} / z^{4} = z^{3-4} = z^{-1}
\]
- For \( y \):
\[
y^{5} / y = y^{5-1} = y^{4}
\]
2. **Combine the Simplified Terms:**
\[
z^{-1} \cdot y^{4} \cdot a^{6}
\]
3. **Express with Positive Exponents:**
Since \( z^{-1} \) is the same as \( \frac{1}{z} \), rewrite the expression as:
\[
\frac{y^{4} a^{6}}{z}
\]
**Final Simplified Form:**
\[
\boxed{\dfrac{y^{4}a^{6}}{z}}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
Let's simplify the expression step by step! First, we can apply the laws of exponents. For the \( z \) terms, we have \( \frac{z^{3}}{z^{4}} = z^{3-4} = z^{-1} \), which we can also write as \( \frac{1}{z} \). Then, for the \( y \) terms, we simplify \( \frac{y^{5}}{y^1} = y^{5-1} = y^{4} \). Putting it all together, we get: \[ \frac{z^{3} y^{5} a^{6}}{z^{4} y} = \frac{1 \cdot y^{4} \cdot a^{6}}{z} = \frac{a^{6} y^{4}}{z} \] So the simplified form of the expression is: \[ \frac{a^{6} y^{4}}{z} \]
