Use the appropriate laws of indices to simplify these expressions.Show the working
a) (4x^2 y^3)^2/(2xy)^3
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.
To simplify the expression (4x^2 y^3)^2 / (2xy)^3 using the laws of indices, we follow these steps:
Step 1: Expand the numerator
(4x^2 y^3)^2 = 16x^4 y^6
Step 2: Expand the denominator
(2xy)^3 = 8x^3 y^3
Step 3: Simplify the expression
(16x^4 y^6) / (8x^3 y^3)
In this case, we can divide the numerator and denominator by the highest power of x and y that appears. In this case, x^3 and y^3.
(16/8) * (x^4 / x^3) * (y^6 / y^3)
=
2 * x^(4-3) * y^(6-3)
=
2xy^3
So, the simplified expression is 2xy^3.