Apply the properties of integer exponents to generate equivalent expressions to (7^-3)^7 x 7^20 / 6^2 with only positive exponents, then solve the expression. Provide the answer as an improper fraction
First, let's apply the property of exponentiation to the expression (7^-3)^7:
(7^-3)^7 = 7^(-3*7) = 7^-21
Next, let's combine this with the expression 7^20:
(7^-3)^7 x 7^20 = 7^-21 x 7^20 = 7^(-21+20) = 7^-1
Now, let's work with the denominator 6^2:
7^-1 / 6^2 = 7^-1 / 6^2 = 7^-1 / (6^2)^1 = 7^-1 / 6^2 = 7^-1 / 36
Since the exponent of 7 is -1, we can write it as 1/7:
1/7 / 36 = 1/7 x 1/36 = 1/252
Therefore, the solution is 1/252, which is an improper fraction.