Question

Can anyone pls solve this.

Answer 1

3)
`((25)^(3/2) * (243)^(3/5))/((16)^(5/4)*(8)^(4/3))`

=>
`((5^2)^(3/2)*(3^5)^(3/5))/((2^4)^(5/4)*(2^3)^(4/3))`

=>
`(5^3*5^3)/(2^5*2^4)`

=>
`(5^6)/(2^9)`

4)
`(3-2√(2) )/(3+2√(2) )`

Multiplying and dividing by conjugate
`3-2√(2)`

=>
`((3-2√(2))(3-2√(2)) )/((3+2√(2))(3-2√(2)))`

=>
`(9-6√(2)-6√(2) +8 )/(9-8)`

=>
`(17-12√(2) )/(1)`

=>
`17-12√(2)`

Comparing it with
`a+b√(2)`, we get

a = 17, b = -12