What is X-^2y(x^3y^5)^3 in simplest form for all values of x and y where the expression is defined?
To simplify the expression X^(-2y) * (x^(3)y^(5))^3, let's first deal with the exponentiation by distributing the exponent to both x and y within the parentheses and simplifying the exponent on X.
First, let's distribute the 3 to both the x^3 and y^5:
(x^3y^5)^3 = (x^3)^3 * (y^5)^3
= x^(3*3) * y^(5*3)
= x^9 * y^15
Next, let's combine this result with the X^(-2y) term:
X^(-2y) * x^9 * y^15
Now we'll combine like terms. When you multiply expressions with the same base, you add the exponents:
X^(-2y) * x^9 = x^(-2y + 9)
Now the expression looks like this:
x^(-2y + 9) * y^15
We cannot simplify any further without knowing the specific values of x and y. However, the expression is simplified as it's now in the form:
x^(9 - 2y) * y^15
This is the simplest form for all values of x and y where the expression is defined, assuming x and y are not zero since we cannot raise 0 to a negative exponent. If x or y were zero, part of the expression would be undefined.