Question

What is the missing exponent? 64/81 = (8/9)?.

Answer 1

Let the ?=x
We have
$\frac{64}{81} = \frac{8}{9}^x$
$\frac{2^6}{3^4}=( \frac{2^3}{3^2} )^x$=$(\frac{2^3}{3^2})^2=( \frac{2^3}{3^2} )^x$
2=x

Answer 2

Try and divide
if (8/9)^m=(64/81), then (8/9) must be a factor of 64/81

basically, if x^m=y, then divide y by x untill you get x

divide top by 8 and bottom by 9 to reverse it
we get 8/9
so therefor 8/9 ties 8/9=64/81
therfor the missing exponent is 2