Problem: 44⋅94⋅49⋅99=4^{4} \cdot 9^{4} \cdot 4^{9} \cdot 9^{9}=44⋅94⋅49⋅99=
Answer Choices:
A. 131313^{13}1313
B. 133613^{36}1336
C. 361336^{13}3613
D. 363636^{36}3636
E. 1296261296^{26}129626
Solution:
44⋅94⋅49⋅99=(4⋅9)4⋅(4⋅9)9=(4⋅9)4+9=3613.4^{4} \cdot 9^{4} \cdot 4^{9} \cdot 9^{9}=(4 \cdot 9)^{4} \cdot(4 \cdot 9)^{9}=(4 \cdot 9)^{4+9}=36^{13}. 44⋅94⋅49⋅99=(4⋅9)4⋅(4⋅9)9=(4⋅9)4+9=3613.
OR\textbf{OR} OR
44⋅94⋅49⋅99=(44+9)⋅(94+9)=413913=(4⋅9)13=36134^{4} \cdot 9^{4} \cdot 4^{9} \cdot 9^{9}=\left(4^{4+9}\right) \cdot\left(9^{4+9}\right)=4^{13} 9^{13}=(4 \cdot 9)^{13}=36^{13} 44⋅94⋅49⋅99=(44+9)⋅(94+9)=413913=(4⋅9)13=3613