[ Pascal's Triangle and the Binomial Theorem ]

Why do the equalities $11^{2}=121$ and $11^{3}=1331$ resemble rows of Pascal's Triangle? What is $11^{4}$?
$11^{2}=(10+1)^{2}=100+2 \cdot 10+1, 11^{3}=(10+1)^{3}=1000+3 \cdot 100+3 \cdot 10+1$.

$11^{4}=C_{4}^{0} \cdot 10^{4}+C_{4}^{1} \cdot 10^{3}+C_{4}^{2} \cdot 10^{2}+C_{4}^{3} \cdot 10+C_{4}^{4}=14641$.

## Answer

$11^{4}=14641$.