Will someone please help me with the answer to the following:

Simplify:
(xy)^-3/(x^-5y)^3

(xy)^-3/(x^-5y)^3

= (1/xy)^3 / ( (1/x^5) y)^3
= (1/x^3(1/y^3) / ( (1/x^15)(y^3) )

= (1/x^3)(1/y^3) (x^15)(1/y^3)
= x^12 / y^6

(xy)^-3 = 1/(x^3y^3)

(x^-5y)^3 = x^-15y^3 = y^3/x^15

So, you have

1/(x^3y^3) / (y^3/x^15)
= 1/(x^3y^3) * x^15/y^3
= x^15/(x^3y^3y^3)
= x^15/(x^3y^6)
= x^12/y^6

Sure, I can help you with that. To simplify the expression (xy)^-3/(x^-5y)^3, we can start by simplifying the numerator and denominator separately, and then divide the simplified numerator by the simplified denominator.

Let's start with simplifying the numerator, (xy)^-3. To do this, we can apply the power rule for exponents. According to the power rule, we can rewrite (xy)^-3 as 1/(xy)^3.

Next, let's simplify the denominator, (x^-5y)^3. To simplify this, we can apply the power rule for exponents as well. The power rule states that when we have an exponent raised to another exponent, we can multiply the exponents. In this case, (-5 * 3) simplifies to -15. Therefore, we can rewrite (x^-5y)^3 as x^-15y^3.

Now that we have simplified the numerator and denominator separately, we can divide the simplified numerator by the simplified denominator. This gives us:

(1/(xy)^3) / (x^-15y^3)

To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction. The reciprocal of x^-15 is x^15. So if we multiply the first fraction by x^15 and the second fraction by 1, we get:

(1/(xy)^3) * (x^15/1) * (1/(x^-15y^3))

Now, let's simplify this expression further. Multiplying the numerators and denominators separately, we get:

(x^15) / (xy)^3 * (1/x^-15y^3)

Next, let's simplify (xy)^3 by applying the power rule again. The power rule states that when we raise a product to a power, we can distribute that power to each factor inside the parentheses. In this case, (xy)^3 becomes x^3y^3.

Now, our expression becomes:

(x^15) / (x^3y^3) * (1/x^-15y^3)

Finally, let's simplify the expression by dividing the exponents of x and y. We subtract the exponent of x in the numerator, x^15, from the exponent of x in the denominator, x^3, which gives us x^(15-3) = x^12. Similarly, we subtract the exponent of y in the numerator, y^3, from the exponent of y in the denominator, y^3, which gives us y^(3-3) = y^0 = 1. Therefore, the simplified expression is:

x^12 / 1

Since any number divided by 1 is equal to the number itself, our final simplified expression is:

x^12

So, the simplified form of (xy)^-3/(x^-5y)^3 is x^12.