To simplify the expression \( y^{-8} \cdot y^{-2} \cdot y^{-5} \), you can use the property of exponents which states that when you multiply powers with the same base, you add their exponents:
\[ y^{-8} \cdot y^{-2} \cdot y^{-5} = y^{-8 + (-2) + (-5)} \]
Now, calculate the sum of the exponents:
\[ -8 - 2 - 5 = -15 \]
So, we have:
\[ y^{-8} \cdot y^{-2} \cdot y^{-5} = y^{-15} \]
To express this with positive exponents, we use the property that \( y^{-n} = \frac{1}{y^n} \):
\[ y^{-15} = \frac{1}{y^{15}} \]
Thus, the fully simplified expression is:
\[ \frac{1}{y^{15}} \]
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