Question

Simplify (y−3)−6\left(y^{-3}\right)^{-6}(y
−3
)
−6

Answer 1

To simplify the expression \((y - 3)^{-6} (y^{-3})^{-6} (y - 3)^{-6}\), we can follow these steps:

1. **Rewrite the expression**:
\[
(y - 3)^{-6} \cdot (y^{-3})^{-6} \cdot (y - 3)^{-6}
\]

2. **Simplify \( (y^{-3})^{-6} \)**:
\[
(y^{-3})^{-6} = y^{3 \cdot 6} = y^{18}
\]

3. **Combine the terms**:
Now replace \( (y^{-3})^{-6} \) in the expression:
\[
(y - 3)^{-6} \cdot y^{18} \cdot (y - 3)^{-6}
\]

4. **Combine the \((y - 3)^{-6}\) terms**:
Since we have two \((y - 3)^{-6}\) factors:
\[
(y - 3)^{-6} \cdot (y - 3)^{-6} = (y - 3)^{-12}
\]

5. **Putting it all together**:
Now we can write the final expression as:
\[
y^{18} \cdot (y - 3)^{-12}
\]

Therefore, the simplified expression is:
\[
\frac{y^{18}}{(y - 3)^{12}}
\]