Question

What is the value of the expression? 9^8/9^-4 times 9^10


`(9^(8))/(9^(-4)) times 9^(10)`


A. 9−48 B. 9−2 C. 92 D. 922

Answer 1

`(9^8)/(9^(-4)* 9^(10)) = (9^8)/(9^(-4+10)) = (9^8)/(9^6) =9^(8-6) = 9^2\\\\a^b * a^c = a^(b+c)\\\frac {a^b}{a^c} =a^(b-c)`

Answer 2

`(9^8)/(9^(-4))\cdot9^(10)=(9^8\cdot9^(10))/(9^(-4))\\----------------\\use:\\a^n\cdot a^m=a^(n+m)\ and\ (a^n)/(a^m)=a^(n-m)\\------------------------\\(9^8\cdot9^(10))/(9^(-4))=(9^(8+10))/(9^(-4))=(9^(18))/(9^(-4))=9^(18-(-4))=9^(18+4)=\huge\boxed{9^(22)}\leftarrow\boxed{D}`


`If\ your\ example\ is:(9^8)/(9^(-4)\cdot9^(10))\ then:\\\\(9^8)/(9^(-4)\cdot9^(10))=(9^8)/(9^(-4+10))=(9^8)/(9^6)=9^(8-6)=\huge\boxed{9^2}\leftarrow\boxed{C}`