Apply the Properties of Integer Exponents to generate equivalent expressions with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents. (4^3 * 7^-2)^-5/ 7^9 * 4^-13

3 answers

To simplify the expression, we can apply the properties of integer exponents.

First, let's start by rearranging the expression to have only positive exponents using the negative exponent property:

(4^3 * 7^-2)^-5 / 7^9 * 4^-13

= (4^3)^-5 * (7^-2)^-5 / 7^9 * 4^-13

Now, let's simplify each term separately:

(4^3)^-5 = 4^(3 * -5) = 4^-15

(7^-2)^-5 = 7^(-2 * -5) = 7^10

4^-13 = 1/4^13 = 1/4^13

Substituting these simplified terms back into the expression, we have:

(4^3 * 7^-2)^-5 / 7^9 * 4^-13

= 4^-15 * 7^10 / 7^9 * 1/4^13

Next, let's simplify the terms with the same base:

4^-15 * 7^10 / 7^9 * 1/4^13

= 7^(10-9) * 4^(-15-13)

= 7^1 * 4^-28

= 7/4^28

Therefore, the simplified fraction is 7/4^28.

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