Answer:

3265173504 / 1953125

Step-by-step explanation:

To simplify the expression (5/8)^(-7) × (7/5)^(-4), we can apply the rule that says: (a^m)^n = a^(m*n). Also, remember that when a number is raised to a negative exponent, it becomes the reciprocal of the number raised to the positive exponent.

So, let's simplify step by step:

(5/8)^(-7) × (7/5)^(-4)

= (8/5)^7 × (5/7)^4 (taking reciprocal)

= (8^7 / 5^7) × (5^4 / 7^4) (expanding the expressions)

Now, let's calculate the values:

= (2097152 / 78125) × (625 / 2401)

= 3265173504 / 1953125

So, the simplified value of the expression is 3265173504 / 1953125.

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