Question

The simplified form of the expression ( -3jk³ / 2k²m³)³ is ( Ajˣkʸ / Bm²) FInd the value of A ,B , x and y?

Answer 1

The simplified form of the expression
`\(\left(-(3jk^3)/(2k^2m^3)\right)^3\)` is
`\(\left((j)/(2m^2)\right)^3\)`. Therefore, the values are A = 1, B = 2, x = 1, and y = -2.

Step-by-step explanation:

To simplify the given expression, we start by cubing the terms inside the parentheses. The cube of
`\(-3jk^3\) is \(-27j^3k^9\)`, and the cube of
`2k^2m^3\) is \(8k^6m^9\)`. By combining these terms and simplifying them, we get
`\(-(27j^3k^3)/(8m^3)\)`. Now, taking the cube root of this expression results in
`\(-(3jk)/(2m)\)`. To make this expression look like
`\((j^xk^y)/(Bm^2)\)`, we set A = 1, B = 2, x = 1, and y = -2. Therefore, the simplified form is
`\(\left((j)/(2m^2)\right)^3\)`, and the values are A = 1, B = 2, x = 1, and y = -2.

In summary, the simplification involves cubing the terms inside the parentheses and then taking the cube root, resulting in a fraction with the desired form. Setting the coefficients and exponents appropriately, we determine the values of A, B, x, and y in the final expression.