a: \(\dfrac{45^{10}\cdot5^{10}}{75^{10}}=\dfrac{225^{10}}{75^{10}}=3^{10}\)
b: \(\dfrac{2^{17}\cdot9^4}{6^3\cdot8^3}=\dfrac{2^{17}\cdot3^8}{2^3\cdot3^3\cdot2^9}=\dfrac{2^{17}}{2^{12}}\cdot3^5=3^5\cdot2^5=6^5=7776\)
c: \(\dfrac{8^{10}+4^{10}}{8^4+4^{11}}=\dfrac{2^{30}+2^{20}}{2^{12}+2^{22}}=\dfrac{2^{20}\cdot\left(2^{10}+1\right)}{2^{12}\left(2^{10}+1\right)}=\dfrac{2^{20}}{2^{12}}=2^8=256\)
`(45^10 . 5^10)/(75^10)`
`= (9^10 . 5^10 . 5^10)/(3^10.25^10)`
`= (9^10 . 25^10)/(3^10.25^10)`
`=(9^10 )/(3^10)`
`= (9/3)^10`
`= 3^10`
`(2^17 . 9^4)/(6^3 .8^3) `
`= (2^17 . 3^8)/(2^3 . 3^3 .2^9) `
`= (2^17 . 3^8)/(2^12 . 3^3 ) `
`= 2^5 . 3^5`
`= 6^5`
`(8^10 + 4^10)/(8^4 +4^11)`
`= (2^30 + 2^20)/(2^12 +2^22)`
`= (2^20.(2^10 + 1))/(2^12 .(1 +2^10))`
`= (2^20)/(2^12)`
`= 2^8`
