Use the appropriate laws of indices to simplify these expressions.Show the working

Question

a) (4x^2 y^3)^2/(2xy)^3

Answer 1

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.