Question

Can someone please help me with my maths question​

Answer 1

`a. \ (625 \cdot m)/(27 \cdot n^(11))`

`b. \ (x^(3 \cdot m - 2))/(y^( 3 + n))`

Explanation:

The question relates with rules of indices

(a) The give expression is presented as follows;

`(m^3 * \left (n^(-2) \right )^4 * (5 \cdot m)^4)/(\left (3 \cdot m^2 \cdot n \right )^3)`

By expanding the expression, we get;

`(m^3 * n^(-8) * 5^4 * m^4)/(\left 3^3 * m^6 * n^3)`

Collecting like terms gives;

`(m^((3 + 4 - 6)) * 5^4)/( 3^3 * n^(3 + 8)) = (625 \cdot m)/(27 \cdot n^(11))`

`(m^3 * \left (n^(-2) \right )^4 * (5 \cdot m)^4)/(\left (3 \cdot m^2 \cdot n \right )^3)= (625 \cdot m)/(27 \cdot n^(11))`

(b) The given expression is presented as follows;

`x^(3 \cdot m + 2) * \left (y^(n - 1) \right )^3 / (x \cdot y^n)^4`

Therefore, we get;

`x^(3 \cdot m + 2) * \left (y^(n - 1) \right )^3 * x^(-4) * y^(-4 \cdot n)`

Collecting like terms gives;

`x^(3 \cdot m + 2 - 4) * \left (y^(3 \cdot n - 3 -4 \cdot n)} \right ) = x^(3 \cdot m - 2) * \left (y^( - 3 -n)} \right ) = x^(3 \cdot m - 2) / \left (y^( 3 + n)} \right )`

`x^(3 \cdot m - 2) / \left (y^( 3 + n)} \right ) = (x^(3 \cdot m - 2))/(y^( 3 + n))`

`x^(3 \cdot m + 2) * \left (y^(n - 1) \right )^3 * x^(-4) * y^(-4 \cdot n) =(x^(3 \cdot m - 2))/(y^( 3 + n))`