The steps involved in simplifying the expression are (xy)^2/x^-3 * (y^3)^-4 = (xy)^2/x^-3 * y^-12 ⇒ x^2y^2/x^-3 * y^-12 ⇒ x^5y^2 * y^-12 ⇒ x^5y^(2 -12) ⇒ x^5y^-10
The statement of the expression is given as:
x multiplied by y to the power of 2 over x to the power of negative 3 multiplied by y to the power of 3, the whole to the power of negative 4
Rewrite the expression, properly
This is done as follows:
(xy)^2/x^-3 * (y^3)^-4
Apply the power rule of indices.
So, we have:
(xy)^2/x^-3 * (y^3)^-4 = (xy)^2/x^-3 * y^-12
Again, we apply the power rule of indices.
So, we have:
(xy)^2/x^-3 * (y^3)^-4 = x^2y^2/x^-3 * y^-12
Evaluate the powers
(xy)^2/x^-3 * (y^3)^-4 = x^5y^2 * y^-12
Again, we apply the power rule of indices.
So, we have:
(xy)^2/x^-3 * (y^3)^-4 = x^5y^(2 -12)
Evaluate the difference
So, we have:
(xy)^2/x^-3 * (y^3)^-4 = x^5y^-10
Hence, the value of the expression (xy)^2/x^-3 * (y^3)^-4 is x^5y^-10
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