Question

Find the area of a rectangle with a length of (4x)^3/2 and a width of 12x^3/4

Answer 1

`\bf Area = length\cdot width\implies A = (4x)^{(3)/(2)}\cdot 12x^{(3)/(4)}\implies A=4^{(3)/(2)}x^{(3)/(2)}\cdot 12x^{(3)/(4)} \\\\\\ A=(2^2)^{(3)/(2)}x^{(3)/(2)}\cdot 12x^{(3)/(4)}\implies A=2^3x^{(3)/(2)}\cdot 12x^{(3)/(4)}\implies A=8x^{(3)/(2)}\cdot 12x^{(3)/(4)} \\\\\\ A=(8\cdot 12)x^{(3)/(2)}\cdot x^{(3)/(4)}\implies A=96x^{(3)/(2)+(3)/(4)}\implies A=96x^{(6+3)/(4)}\implies A=96x^{(9)/(4)}`