Question

решите используя свойства степеней​

Answer 1

$1) \ \dfrac{100\cdot2^{n}\cdot(5^{2})^{n}}{2^{n-2}\cdot5^{2n+1}} =\dfrac{5^{2}\cdot2^{2} \cdot2^{n}\cdot5^{2n}}{2^{n-2}\cdot5^{2n+1}}=5^{2+2n-2n-1}\cdot2^{2+n-n+2}=\\\\=5^{1}\cdot2^{4} =5\cdot16=\boxed{80}\\\\\\2) \ \dfrac{15^{n}\cdot3^{2}\cdot(5^{n+1})^{2}}{3^{n}\cdot(5^{n})^{3} \cdot3\cdot5 } =\dfrac{3^{n}\cdot 5^{n}\cdot3^{2}\cdot5^{2n+2}}{3^{n}\cdot5^{3n} \cdot3\cdot5 }=3^{n+2-n-1}\cdot5^{n+2n+2-3n-1} =\\\\=3^{1}\cdot5^{1}=3\cdot5=\boxed{15}$

$3) \ \dfrac{147\cdot(7^{n})^{2}\cdot9^{n}\cdot3^{2}}{3^{2n+2}\cdot7^{2n+1}}=\dfrac{3\cdot7^{2} \cdot7^{2n}\cdot3^{2n}\cdot3^{2}}{3^{2n+2}\cdot7^{2n+1}}= \\\\\\=3^{1+2n+2-2n-2}\cdot7^{2+2n-2n-1}=3^{1}\cdot7^{1} =3\cdot7=\boxed{21}$