Question

SOLVE THE EQUATIONS BY INTRODUCING A SUBSTITUITION THAT TRANSFORMS THESE EQUATIONS TO QUADRATIC FORM
A)(5x+3)^(5/3)=32
B)(x+2)^(4/3)=16
C)(x+1)^(2/3)=4
D)(x-7)^(4/3)=81

Answer 1

A) 
$(5 x + 3)^{5/3}=32=2^5 \\\\(5x+3)=(2^{5})^{3/5}=2\\\\x=1$

B)
$(x+2)^{4/3}=16\\\\(x+2)^4=(2^4)^3=2^{12}\\\\(x+2)^2=+2^6\ as\ \ -2^6\ not\ possible.\\\\(x+2)=+2^3\ or\ -2^3 \\\\x=+6\ or\ -10$

you can expand (x+2)^2  to have quadratic form.

C)
       (X+1)^2 = 4^3=64
       x + 1  = + 8 or  - 8 
       x = - 9  or  + 7
   you can do this by expanding  x+1)^2 also

d)
    (x-7)^4 = 81^3 = 3^12
         (x - 7)^2 =  + 3^6
           x - 7  =  + 3^3 or  - 3^3
       x = 34 or  - 20