Apply the Properties of Integer Exponents to generate equivalent expressions to (7−3)7 ⋅ 7206−2 with only positive exponents, then solve the expression. Provide the answer as an improper fraction.(1 point)

Question

(7−3)7 ⋅ 7206−2=

Answer 1

To apply the properties of integer exponents, we use the following rules:

1. a^m ⋅ a^n = a^(m+n)
2. (a^m)^n = a^(m*n)
3. (a⋅b)^n = a^n ⋅ b^n

Using these rules, we can simplify the expression (7^-3)7 ⋅ 7206^-2 as follows:

(7^-3)7 ⋅ 7206^-2
= 7^-3 ⋅ 7 ⋅ 7206^-2
= (7^-3 ⋅ 7) ⋅ (7206^-2)
= 7^(-3+1) ⋅ (720^6)^-2
= 7^-2 ⋅ (720^6)^-2

Now, let's solve the expression:

7^-2 ⋅ (720^6)^-2
= (1/7^2) ⋅ (1/720^6)^2
= 1/49 ⋅ 1/(720^12)
= 1/(49 * 720^12)

Therefore, the expression (7−3)7 ⋅ 7206−2 is equivalent to 1/(49 * 720^12) as an improper fraction.