Question

Simplify :
12⁷*28⁶
_______
21⁷*16⁶​

Answer 1

Explanation:

Prime factorize 12 , 28 , 21 and 16

12 = 2 * 2 * 3 = 2² * 3

28 = 2 * 2 * 7 = 2² *7

21 = 3 * 7

16 = 2 * 2 * 2 * 2 = 2⁴

`(12^(7)*28^(6))/(21^(7)*16^(6))=((2^(2)*3)^(7)*(2^(2)*7)^(6))/((3*7)^(7)*(2^(4))^(6))\\\\\\\\=(2^(2*7)*3^(7)*2^(2*6)*7^(6))/(3^(7)*7^(7)*2^(4*6))\\\\\\=(2^(14)*3^(7)*2^(12)*7^(6))/(3^(7)*7^(7)*2^(24))\\\\\\=(2^(14+12-24)*3^(7-7))/(7^(7-6))\\\\\\=(2^(2)*3^(0))/(7^(1))\\\\\\=(2^(2))/(7)`

Hint:

`a^(m)*a^(n)=a^(m+n)\\\\\\(a^(m))^(n)=a^(m*n)\\\\(a^(m))/(a^(n))=a^(m-n) \ if \ m >n\\\\\\(a^(m))/(a^(n))=(1)/(a^(n-m)) \ if \ n>m`