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)² = (2•5)² = 2² • 5²

Equation at the end of step  1  :

   128         64
  (———•(104))+(——•(22•52))
   100         10

Step  2  :

            32
 Simplify   ——
            5 

Equation at the end of step  2  :

   128              32
  (——— • (104)) +  (—— • (22•52))
   100              5 

Step  3  :

Multiplying exponents :

 3.1    2⁵  multiplied by  2²   = 2^{(5 + 2)} = 2⁷

Raising to a Power :

 3.2    5²   divided by   5¹   = 5^{(2 - 1)} = 5¹ = 5

Equation at the end of step  3  :

   128              
  (——— • (104)) +  640
   100              

Step  4  :

 4.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  4  :

   128                 
  (——— • (24•54)) +  640
   100                 

Step  5  :

            32
 Simplify   ——
            25

Equation at the end of step  5  :

   32                 
  (—— • (24•54)) +  640
   25                 

Step  6  :

Multiplying exponents :

 6.1    2⁵  multiplied by  2⁴   = 2^{(5 + 4)} = 2⁹

Dividing exponents :

 6.2    5⁴   divided by   5²   = 5^{(4 - 2)} = 5²

Equation at the end of step  6  :

  (29•52) +  640

Step  7  :

Step  8  :

Pulling out like terms :

 8.1     Pull out like factors :

   2⁹ • 5² + 640  =   32 • (1 + 20) 

Final result :

  32 • (1 + 20)