Question

Can anyone pls solve this.

Answer 1

Answer:

3) $\frac{(25)^{3/2} * (243)^{3/5}}{(16)^{5/4}*(8)^{4/3}}$

=> $\frac{(5^2)^{3/2}*(3^5)^{3/5}}{(2^4)^{5/4}*(2^3)^{4/3}}$

=> $\frac{5^3*5^3}{2^5*2^4}$

=> $\frac{5^6}{2^9}$

4) $\frac{3-2\sqrt{2} }{3+2\sqrt{2} }$

Multiplying and dividing by conjugate $3-2\sqrt{2}$

=> $\frac{(3-2\sqrt{2})(3-2\sqrt{2}) }{(3+2\sqrt{2})(3-2\sqrt{2})}$

=> $\frac{9-6\sqrt{2}-6\sqrt{2} +8 }{9-8}$

=> $\frac{17-12\sqrt{2} }{1}$

=> $17-12\sqrt{2}$

Comparing it with $a+b\sqrt{2}$, we get

a = 17, b = -12