Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-4" was replaced by "^(-4)".

(2): "6." was replaced by "(6/1)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  1  :

   16 6
  (——•—)•(25•55)
   10 1

Step  2  :

            6
 Simplify   —
            1

Equation at the end of step  2  :

   16   (10-4)
  (—— • ——————) • (25•55)
   10     6   

Step  3  :

 3.1     10 = 2•5

(10)^-4 = (2•5)^(-4) = (2)^(-4) • (5)^(-4)

Equation at the end of step  3  :

   16   ((2)(-4)•(5)(-4)) 
  (—— • —————————————————) • (25•55)
   10           6        

Step  4  :

            1         
 Divide  ———————  by  6
         (24•54)      

Multiplying exponents :

 4.1    2⁴  multiplied by  2¹   = 2^{(4 + 1)} = 2⁵

Equation at the end of step  4  :

   16       1    
  (—— • —————————) • (25•55)
   10   (25•54•3)

Step  5  :

            8
 Simplify   —
            5

Equation at the end of step  5  :

   8       1    
  (— • —————————) • (25•55)
   5   (25•54•3)

Step  6  :

Multiplying exponents :

 6.1    5¹  multiplied by  5⁴   = 5^{(1 + 4)} = 5⁵

Dividing exponents :

 6.2    2³   divided by   2⁵   = 2^{(3 - 5)} = 2^(-2) = ¹/_2²

Equation at the end of step  6  :

      1    
  ————————— • (25•55)
  (55•22•3)

Step  7  :

Dividing exponents :

 7.1    2⁵   divided by   2²   = 2^{(5 - 2)} = 2³

Canceling Out :

 7.2      Canceling out  5⁵ as it appears on both sides of the fraction line

Final result :

  8           
  — = 2.66667 
  3