Question

Simplify the following expressions

X2 X-2/3

X1/4/ X-5/2

(4/5)x-2/5 y3/2 / (2/3) x3/5y1/2

(2/3)x2/3y2/3 / (1/3)x-1/3y-1/3

(z2/3 x2/3y-2/3 ) y + (z2/3 x-1/3y-1/3 ) x

(4x3/5y3 z2 ) 1/3

Answer 1

Explanation:

For each case we have the next step by step solution.

1. 
   `x^2((x-2)/(3))=(x^3-2x^2)/(3)`
2. 
   `(x^(1/4))/(x-(5)/(2))=(x^(1/4))/((2x)/(2)-(5)/(2))=(x^(1/4))/((2x-5)/(2))=\frac{2x^(1/4)}{{2x-5}}`
3. 
   `((4)/(5)x-(2)/(5)y^(3/2))/(((2)/(3)x^3)/(5y^(1/2)))=((4x)/(5)-(2y^(3/2))/(5))/(((2x^3)/(3))/(5y^(1/2)))=((4x-2y^(3/2))/(5))/((2x^3)/(15y^(1/2)))={((4x-2y^(3/2))\cdot 15y^(1/2))/(5\cdot 2x^3)}`
   `{((4x-2y^(3/2))\cdot 15y^(1/2))/(5\cdot 2x^3)}={((60xy^(1/2)-30y^(3/2)y^(1/2)))/(10x^3)}={((60xy^(1/2)-30y^(4/2)))/(10x^3)}={((60xy^(1/2)-30y^(2)))/(10x^3)}`
4. 
   `(((2)/(3)x^2)/(3y^(2/3)))/((1)/(3)x-(1)/(3)y-(1)/(3))=(((2x^2)/(3))/(3y^(2/3)))/((x)/(3)-(y)/(3)-(1)/(3))=((2x^2)/(9y^(2/3)))/((x-y-1)/(3))=(2x^2\cdot 3)/((x-y-1)\cdot 9y^(2/3))}=(6x^2)/((9xy^(2/3)-9yy^(2/3)-9y^(2/3)))}=(6x^2)/((9xy^(2/3)-9y^(5/3)-9y^(2/3)))}`
5. 
   `(z^(2/3)x^(2/3)y+(2)/(3))y+(z^(2/3)x-(1)/(3)y-(1)/(3))x=(z^(2/3)x^(2/3)y^2+(2)/(3)y)+(z^(2/3)x^2-(1)/(3)yx-(x)/(3))=z^(2/3)x^(2/3)y^2+z^(2/3)x^2-(1)/(3)yx+(2)/(3)y-(x)/(3)`
6. 
   `((4x^3)/(5y^2)z^2)^(1/3)=((4x^3)^(1/3))/((5y^2)^(1/3))(z^2)^(1/3)=(4^(1/3)x)/(5^(1/3)y^(2/3))z^(2/3)`