Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "6.4" was replaced by "(64/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)⁶ = (2•5)⁶ = 2⁶ • 5⁶

Equation at the end of step  1  :

   38       64
  (——•(102))——•(26•56))
   10(      10

Step  2  :

            32
 Simplify   ——
            5 

Equation at the end of step  2  :

   38             32
  (—— • (102)) ÷ (—— • (26•56))
   10             5 

Step  3  :

Multiplying exponents :

 3.1    2⁵  multiplied by  2⁶   = 2^{(5 + 6)} = 2¹¹

Raising to a Power :

 3.2    5⁶   divided by   5¹   = 5^{(6 - 1)} = 5⁵

Equation at the end of step  3  :

   38
  (—— • (102)) ÷ (211•55)
   10

Step  4  :

 4.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  4  :

   38
  (—— • (22•52)) ÷ (211•55)
   10

Step  5  :

            19
 Simplify   ——
            5 

Equation at the end of step  5  :

  19
  —— • (22•52)) ÷ (211•55)
  5 

Step  6  :

Dividing exponents :

 6.1    5²   divided by   5¹   = 5^{(2 - 1)} = 5¹ = 5

Equation at the end of step  6  :

Step  7  :

               380  
 Simplify   ————————
            (211•55) 

Dividing exponents :

 7.1    2²   divided by   2¹¹   = 2^{(2 - 11)} = 2^(-9) = ¹/_2⁹

Dividing exponents :

 7.2    5¹   divided by   5⁵   = 5^{(1 - 5)} = 5^(-4) = ¹/_5⁴

Final result :

     19             
  ——————— = 0.00006 
  (29•54)