Question
6. \( \frac{3\left(x y^{6}\right)^{0}}{-6 y^{2}} \)
Ask by Spencer Bernard. in South Africa
Mar 08,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified expression is \( -\frac{1}{2y^2} \).
Solution
1. Recall that any nonzero expression raised to the power \(0\) equals \(1\). Thus,
\[
(xy^6)^0 = 1.
\]
2. Substitute back into the expression:
\[
\frac{3 \cdot 1}{-6y^2} = \frac{3}{-6y^2}.
\]
3. Simplify the coefficient:
\[
\frac{3}{-6} = -\frac{1}{2},
\]
so the expression becomes
\[
-\frac{1}{2} \cdot \frac{1}{y^2}.
\]
4. Combine the terms to get the final result:
\[
-\frac{1}{2y^2}.
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
Any expression raised to the power of zero equals one, provided that the base is not zero. Therefore, \( \left(x y^{6}\right)^{0} = 1 \). This simplifies your original expression to: \[ \frac{3 \cdot 1}{-6y^{2}} = \frac{3}{-6y^{2}} = -\frac{1}{2y^{2}}. \] So the simplified form is: \[ -\frac{1}{2y^{2}}. \] If you're looking for clarity in your calculations, remember that powers of zero are a trusty travel companion in math – they always lead you back to one! Just like packing light for a trip, simplifying might take some items out of the equation but makes everything easier to handle.
