[tex]\big9^5\cdot\big5^9:4\big5^5=\dfrac{9^5\cdot5^9}{45^5}=\dfrac{9^5\cdot5^9}{(9\cdot5)^5}=\dfrac{9^5\cdot5^9}{9^5\cdot5^5}=\dfrac{9^5}{9^5}\cdot\dfrac{5^9}{5^5}=1\cdot\big5^{9-5}=\big5^4=625[/tex]
[tex]9^5\cdot5^9:45^5=9^5\cdot5^{5+4}:45^5=9^5\cdot5^5\cdot5^4:45^5= (9\cdot5)^5\cdot5^4:45^5=\\\\=45^5\cdot5^4:45^5=5^4\cdot45^5\cdot\dfrac1{45^5}=5^4\cdot1=625[/tex]
