Apply the properties of integer exponents to generate equivalent expressions to (4^3 7^-2)^-5 over 7^9 / 4^-13 with only positive exponents then solve the expression, the answer will be a simplified fraction with no remaining exponents

Answer 1

Let's break down the given expression and simplify it step by step.

1. (4^3 7^-2)^-5:
By applying the property of exponents, we can multiply the exponents within the parentheses:
(4^3 7^-2)^-5 = 4^(3*-5) 7^(-2*-5) = 4^(-15) 7^10

2. 7^9 / 4^-13:
To simplify this expression, we can change the negative exponent to a positive exponent by applying the property of exponents:
7^9 / 4^-13 = 7^9 / (1/4^13) = 7^9 4^13

Now, let's combine the two expressions:
(4^3 7^-2)^-5 / (7^9 / 4^-13) = (4^(-15) 7^10) / (7^9 4^13)

Using the property of exponents, we can divide the exponents with the same base inside the parentheses:
(4^(-15) 7^10) / (7^9 4^13) = 4^(-15-13) 7^(10-9) = 4^-28 7^1

Finally, we simplify the expression:
4^-28 7^1 = 1/4^28 * 7 = 7/4^28

The simplified fraction is 7/4^28.

Answer 2

the answer is 7 / 16