Question
Simplify. \[ \frac{y^{-6}}{y^{-4}} \] Write your answer with a positive exponent only.
Ask by Cook Stuart. in the United States
Jan 29,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\(\frac{1}{y^2}\)
Solution
To simplify the expression \(\frac{y^{-6}}{y^{-4}}\) with only positive exponents, follow these steps:
1. **Subtract the Exponents:**
\[
\frac{y^{-6}}{y^{-4}} = y^{-6 - (-4)} = y^{-2}
\]
2. **Convert to Positive Exponent:**
\[
y^{-2} = \frac{1}{y^2}
\]
So, the simplified expression with a positive exponent is:
\[
\frac{1}{y^2}
\]
Answer:
\(\dfrac{1}{\,y^{2}\,}\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To simplify the expression \(\frac{y^{-6}}{y^{-4}}\), we can use the property of exponents that states \(\frac{a^m}{a^n} = a^{m-n}\). Applying this, we get: \[ \frac{y^{-6}}{y^{-4}} = y^{-6 - (-4)} = y^{-6 + 4} = y^{-2}. \] Now, to express this with a positive exponent, we use the property that \(a^{-m} = \frac{1}{a^m}\): \[ y^{-2} = \frac{1}{y^2}. \] So, the simplified expression is: \[ \frac{1}{y^2}. \]
