Which expression is equivalent to 40x^-3y^5/8x^-2y^-2 for all values for x and y where the expression is defined?
A. 5xy^7
B. 5x^5y^7
C. 5/xy^7
D. 5y^7/x
To simplify the expression, we can combine the like terms in the numerator and the denominator.
In the numerator, we have 40x^(-3)y^5, which can be rewritten as (40/x^3)y^5.
In the denominator, we have 8x^(-2)y^(-2), which can be rewritten as (8/x^2)(1/y^2).
Now we can rewrite the expression as (40/x^3)y^5 / (8/x^2)(1/y^2).
Next, we can simplify the expression by canceling out common factors between the numerator and the denominator.
Canceling out the x^2 and x^3 terms in the numerator and the denominator, we get:
40y^5 / 8 * 1/y^2.
Simplifying further, we have:
40y^5 / (8/y^2) = 40y^5 * y^2 / 8.
Multiplying the terms, we get:
(40 * y^5 * y^2) / 8 = (40 * y^(5+2)) / 8 = (40 * y^7) / 8.
Finally, we can simplify the expression by dividing 40 and 8:
(40 * y^7) / 8 = 5y^7.
Therefore, the expression is equivalent to 5y^7.
Answer: \boxed{A) 5xy^7}.