Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-6" was replaced by "^(-6)".

(2): "2.7" was replaced by "(27/10)". 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  :

   78          27
  (——•(10-6))•(——•(25•55))
   10          10

Step  2  :

            27
 Simplify   ——
            10

Equation at the end of step  2  :

   78              27
  (—— • (10-6)) • (—— • (25•55))
   10              10

Step  3  :

Dividing exponents :

 3.1    2⁵   divided by   2¹   = 2^{(5 - 1)} = 2⁴

Raising to a Power :

 3.2    5⁵   divided by   5¹   = 5^{(5 - 1)} = 5⁴

Equation at the end of step  3  :

   78
  (—— • (10-6)) • (33•24•54)
   10

Step  4  :

 4.1     10 = 2•5

(10)^-6 = (2•5)^(-6) = (2)^(-6) • (5)^(-6)

Equation at the end of step  4  :

   78
  (—— • ((2)(-6)•(5)(-6))) • (33•24•54)
   10

Step  5  :

            39
 Simplify   ——
            5 

Equation at the end of step  5  :

   39
  (—— • ((2)(-6)•(5)(-6))) • (33•24•54)
   5 

Step  6  :

Multiplying exponents :

 6.1    5¹  multiplied by  5⁶   = 5^{(1 + 6)} = 5⁷

Equation at the end of step  6  :

     39  
  ——————— • (33•24•54)
  (57•26)

Step  7  :

Multiplying exponents :

 7.1    3¹  multiplied by  3³   = 3^{(1 + 3)} = 3⁴

Dividing exponents :

 7.2    2⁴   divided by   2⁶   = 2^{(4 - 6)} = 2^(-2) = ¹/_2²

Dividing exponents :

 7.3    5⁴   divided by   5⁷   = 5^{(4 - 7)} = 5^(-3) = ¹/_5³

Final result :

  1053           
  ———— = 2.10600 
  500