Firstly, we can simplify the denominator by using the law of indices that states when dividing with the same base, you subtract the powers. So,
(4x^2 y^3)^2/(2xy)^3 = (4x^2 y^3)^2/2^3 x^3 y^3
Next, we can simplify the numerator by using the law of indices that states when raising a power to a power, you multiply the powers. So,
(4x^2 y^3)^2/2^3 x^3 y^3 = 16x^4 y^6/8x^3 y^3
Now, we can simplify further by canceling out common factors in the numerator and denominator. We can cancel out a factor of 2, x^3, and y^3. So,
16x^4 y^6/8x^3 y^3 = 2x y^3.
Therefore, (4x^2 y^3)^2/(2xy)^3 simplifies to 2x y^3.
Use the appropriate laws of indices to simplify these expressions.Show the working
a) (4x^2 y^3)^2/(2xy)^3
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