To simplify the expression \((y^4/y^2)^2 \cdot (y^8/y^6)^2\), we can simplify each part step-by-step.
-
Simplify \((y^4/y^2)^2\): \[ y^4/y^2 = y^{4-2} = y^2 \] Then raise it to the power of 2: \[ (y^2)^2 = y^{2 \cdot 2} = y^4 \]
-
Simplify \((y^8/y^6)^2\): \[ y^8/y^6 = y^{8-6} = y^2 \] Then raise it to the power of 2: \[ (y^2)^2 = y^{2 \cdot 2} = y^4 \]
-
Combine the results: Now we multiply the two simplified results: \[ y^4 \cdot y^4 = y^{4+4} = y^8 \]
Thus, the simplified expression is: \[ \boxed{y^8} \]