已知3^2m=5 3^n=10 求(1)9^m-n (2)9^2m-nThank you!

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已知3^2m=5 3^n=10 求(1)9^m-n (2)9^2m-nThank you!
已知3^2m=5 3^n=10 求(1)9^m-n (2)9^2m-n
Thank you!

已知3^2m=5 3^n=10 求(1)9^m-n (2)9^2m-nThank you!
(1)
9^(m-n)
=9^m÷9^n
=3^(2m)÷(3^n)²
=5÷10²
=1/20
(2)
9^(2m-n)
=9^(2m)÷9^n
=(3^2m)²÷(3^n)²
=5²÷10²
=1/4

9^m-n=9^m/9^n=(3^2)^m/(3^2)^n=3^2m/(3^n)^2=5/10^2=1/20
9^2m-n=9^2m/9^n=(3^2m)^2/(3^n)^2=5^2/10^2=1/4

3^2m=9^m=5,9^m-n =9^m / 9^m- 9^n
3^n=10, 9^n=100,
9^(m-n )=5/100=0.05
9^2m= 5^2 =25,
9^(2m-n)=0.25
LZ得加括号..不然指数项很困扰