Question

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

Answer 1

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