Question

Simplify:

(18/16)^3/4 × (25/9)^3/2

(x + 1/2) (x + 3/2)

URGENT!!!!

Answer 1

$(\frac{18}{16})^\frac{3}{4} * (\frac{25}{9})^\frac{3}{2} \\ \\ (\frac{2*3*3}{2*2*2*2})^\frac{3}{4} * (\frac{5*5}{3*3})^\frac{3}{2} \\ \\ (\frac{2*3^2}{2^4})^\frac{3}{4} * (\frac{5^2}{3^2})^\frac{3}{2} \\ \\ (\frac{3^2}{2^3})^\frac{3}{4}*(\frac{5^{2*\frac{3}{2}}}{3^{2*\frac{3}{2}}})$


$\frac{3^{2*\frac{3}{4}}}{2^{3*\frac{3}{4}}} * \frac{5^3}{3^3} \\ \\ \frac{3^{\frac{3}{2}}}{2^{\frac{9}{4}}} * \frac{5^3}{3^3} \\ \\ \frac{5^3}{2^{\frac{9}{4}}*3^{3-\frac{3}{2}}} \\ \\ \frac{5^3}{2^{\frac{9}{4}}*3^{\frac{3}{2}}} \\ \\ 5^3 * 2^{-9/4} * 3^{-3/2}$

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$(x+\frac{1}{2} ) (x + \frac{3}{2} ) \\ \\ x^2 + \frac{3}{2} x + \frac{1}{2} x + \frac{1}{2}*\frac{3}{2} \\ \\ x^2 + (\frac{3}{2}+\frac{1}{2})x+\frac{3}{4} \\ \\ x^2 + \frac{4}{2} x + \frac{3}{4} \\ \\ x^2 + 2 x + \frac{3}{4}$