What is the least possible value of the expression if two of the values 1, 2, 4, and 8 are substituted in any order for the variables x and y?

1/9^x÷9^y=9^z
Enter a power of 9 in the box.

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To find the least possible value of the expression 1/9^x ÷ 9^y = 9^z, we need to consider all possible combinations of x and y from the given values 1, 2, 4, and 8.

First, we substitute each combination into the expression and simplify:

1/9^1 ÷ 9^2 = 9^z
1/9 ÷ 81 = 9^z
1/729 = 9^z

1/9^1 ÷ 9^4 = 9^z
1/9 ÷ 6561 = 9^z
1/59049 = 9^z

1/9^1 ÷ 9^8 = 9^z
1/9 ÷ 43046721 = 9^z
1/387420489 = 9^z

1/9^2 ÷ 9^1 = 9^z
1/81 ÷ 9 = 9^z
1/729 = 9^z

1/9^2 ÷ 9^4 = 9^z
1/81 ÷ 6561 = 9^z
1/531441 = 9^z

1/9^2 ÷ 9^8 = 9^z
1/81 ÷ 43046721 = 9^z
1/3486784401 = 9^z

1/9^4 ÷ 9^1 = 9^z
1/6561 ÷ 9 = 9^z
1/59049 = 9^z

1/9^4 ÷ 9^2 = 9^z
1/6561 ÷ 81 = 9^z
1/59049 = 9^z

1/9^4 ÷ 9^8 = 9^z
1/6561 ÷ 43046721 = 9^z
1/3486784401 = 9^z

1/9^8 ÷ 9^1 = 9^z
1/43046721 ÷ 9 = 9^z
1/387420489 = 9^z

1/9^8 ÷ 9^2 = 9^z
1/43046721 ÷ 81 = 9^z
1/531441 = 9^z

1/9^8 ÷ 9^4 = 9^z
1/43046721 ÷ 6561 = 9^z
1/6561 = 9^z

From these calculations, we can see that the least possible value of the expression is 1/3486784401 when x = 2, y = 8, and z = -2.

Therefore, the least possible value of the expression is 1/3486784401.

1/9^x = 9^-x

9^-x /9^y = 9^-x * 9^-y = 9^-(x+y)
so
z = -(x+y)
4 asnd 8 gives
z = -12
and 9^-12 is about as small as we are going to get