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)
(7^−3)^7 ⋅ 7^20/6^−2= blank
fill in the blank
To generate equivalent expressions with positive exponents, we can use the property that states (a^m)^n = a^(m*n). Let's apply this property to the expression:
(7^(-3))^7 ⋅ 7^(20)/6^(-2)
Using the property, we have:
7^((-3)*7) ⋅ 7^(20)/6^(-2)
Simplifying the exponents:
7^(-21) ⋅ 7^(20)/6^(-2) = 7^(-21+20)/6^(-2)
Now, applying the property that states a^(-n) = 1/a^n for any non-zero number a, we have:
7^(-21+20)/6^(-2) = 7^(-1)/6^(-2)
Finally, using the property that states a^(-n) = 1/a^n, we can rewrite the expression as:
1/7^1 * 6^2 = 1/7 * 36 = 36/7
Therefore, the answer is 36/7 as an improper fraction.