simplify (4xy^2)^3(xy)^5'
a ) 64x^8y^11
b ) 64x^15y^30
c ) 12x^2y^11
d ) 12x^8y^11
To simplify (4xy^2)^3(xy)^5, we first apply the exponent outside the parentheses to each term inside, and then multiply the exponents when we have the same base.
(4xy^2)^3 = 4^3 * (x)^3 * (y^2)^3 = 64x^3y^6
(xy)^5 = (x)^5 * (y)^5 = x^5 * y^5
Now, let's multiply the two simplified expressions:
64x^3y^6 * x^5y^5 = 64 * x^3 * x^5 * y^6 * y^5 = 64x^8y^11
Therefore, the simplified form of (4xy^2)^3(xy)^5 is 64x^8y^11, which corresponds to option a).