Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.2" was replaced by "(12/10)". 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  :

   72       12
  (——•(103))——•(25•55))
   10(      10

Step  2  :

            6
 Simplify   —
            5

Equation at the end of step  2  :

   72             6
  (—— • (103)) ÷ (— • (25•55))
   10             5

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2⁵   = 2^{(1 + 5)} = 2⁶

Raising to a Power :

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

Equation at the end of step  3  :

   72
  (—— • (103)) ÷ (26•3•54)
   10

Step  4  :

 4.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  4  :

   72
  (—— • (23•53)) ÷ (26•3•54)
   10

Step  5  :

            36
 Simplify   ——
            5 

Equation at the end of step  5  :

  36
  —— • (23•53)) ÷ (26•3•54)
  5 

Step  6  :

Multiplying exponents :

 6.1    2²  multiplied by  2³   = 2^{(2 + 3)} = 2⁵

Dividing exponents :

 6.2    5³   divided by   5¹   = 5^{(3 - 1)} = 5²

Equation at the end of step  6  :

Step  7  :

               7200  
 Simplify   —————————
            (26•3•54)

Dividing exponents :

 7.1    2⁵   divided by   2⁶   = 2^{(5 - 6)} = 2^(-1) = ¹/_2¹ = ¹/₂

Dividing exponents :

 7.2    3²   divided by   3¹   = 3^{(2 - 1)} = 3¹ = 3

Dividing exponents :

 7.3    5²   divided by   5⁴   = 5^{(2 - 4)} = 5^(-2) = ¹/_5²

Final result :

   3           
  —— = 0.06000 
  50