Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.077" was replaced by "(077/1000)".

Step  1  :

 1.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  1  :

                   77 
  (4 • (105)) -  (———— • (25•55))
                  1000

Step  2  :

             77 
 Simplify   ————
            1000

Equation at the end of step  2  :

                   77 
  (4 • (105)) -  (———— • (25•55))
                  1000

Step  3  :

Dividing exponents :

 3.1    2⁵   divided by   2³   = 2^{(5 - 3)} = 2²

Raising to a Power :

 3.2    5⁵   divided by   5³   = 5^{(5 - 3)} = 5²

Equation at the end of step  3  :

  (4 • (105)) -  7700

Step  4  :

 4.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  4  :

  (4 • (25•55)) -  7700

Step  5  :

Multiplying exponents :

 5.1    2²  multiplied by  2⁵   = 2^{(2 + 5)} = 2⁷

Equation at the end of step  5  :

  (27•55) -  7700

Step  6  :

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   2⁷ • 5⁵ - 7700  =   4 • (1 - 1925) 

Final result :

  4 • (1 - 1925)