Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.5" was replaced by "(25/10)".

Step  1  :

 1.1     10 = 2•5

(10)⁸ = (2•5)⁸ = 2⁸ • 5⁸

Equation at the end of step  1  :

   25
  (—— • (105)) ÷ (5 • (28•58))
   10

Step  2  :

Raising to a Power :

 2.1    5¹  multiplied by  5⁸   = 5^{(1 + 8)} = 5⁹

Equation at the end of step  2  :

   25
  (—— • (105)) ÷ (59•28)
   10

Step  3  :

 3.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  3  :

   25
  (—— • (25•55)) ÷ (59•28)
   10

Step  4  :

            5
 Simplify   —
            2

Equation at the end of step  4  :

  5
  — • (25•55)) ÷ (59•28)
  2

Step  5  :

Multiplying exponents :

 5.1    5¹  multiplied by  5⁵   = 5^{(1 + 5)} = 5⁶

Dividing exponents :

 5.2    2⁵   divided by   2¹   = 2^{(5 - 1)} = 2⁴

Equation at the end of step  5  :

Step  6  :

            (56•24)
 Simplify   ———————
            (59•28)

Dividing exponents :

 6.1    5⁶   divided by   5⁹   = 5^{(6 - 9)} = 5^(-3) = ¹/_5³

Dividing exponents :

 6.2    2⁴   divided by   2⁸   = 2^{(4 - 8)} = 2^(-4) = ¹/_2⁴

Final result :

    1            
  ———— = 0.00050 
  2000