Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-1" was replaced by "^(-1)".

Step  1  :

 1.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  1  :

     (84) 
  {———————}-1 ÷ 4
   (24•54)

Step  2  :

 2.1     8 = 23

(8)⁴ = (2³)⁴ = 2¹²

Equation at the end of step  2  :

     212  
  {———————}-1 ÷ 4
   (24•54)

Step  3  :

              212  
 Simplify   ———————
            (24•54)

Raising to a Power :

 3.1    2¹²   divided by   2⁴   = 2^{(12 - 4)} = 2⁸

Equation at the end of step  3  :

  256
 (———)-1) ÷ 4
  625

Step  4  :

 4.1     256 = 28

(256)^-1 = (2⁸)^(-1) = (2)^(-8)  4.2     625 = 5⁴ (625)^-1 = (5⁴)^(-1) = (5)^(-4)

Equation at the end of step  4  :

  (2)(-8)
  ——————— ÷ 4
  (5)(-4)

Step  5  :

         (2)(-8)      
 Divide  ———————  by  4
         (5)(-4)      

Multiplying exponents :

 5.1    2²  multiplied by  2⁸   = 2^{(2 + 8)} = 2¹⁰

Final result :

   625           
  ———— = 0.61035 
  1024