Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-5" was replaced by "^(-5)".

(2): "6.02" was replaced by "(602/100)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  1  :

   32          602
  (——•(10-5))•(———•(23•53))
   10          100

Step  2  :

            301
 Simplify   ———
            50 

Equation at the end of step  2  :

   32              301
  (—— • (10-5)) • (——— • (23•53))
   10              50 

Step  3  :

Dividing exponents :

 3.1    2³   divided by   2¹   = 2^{(3 - 1)} = 2²

Raising to a Power :

 3.2    5³   divided by   5²   = 5^{(3 - 2)} = 5¹ = 5

Equation at the end of step  3  :

   32
  (—— • (10-5)) • 6020
   10

Step  4  :

 4.1     10 = 2•5

(10)^-5 = (2•5)^(-5) = (2)^(-5) • (5)^(-5)

Equation at the end of step  4  :

   32
  (—— • ((2)(-5)•(5)(-5))) • 6020
   10

Step  5  :

            16
 Simplify   ——
            5 

Equation at the end of step  5  :

   16
  (—— • ((2)(-5)•(5)(-5))) • 6020
   5 

Step  6  :

Multiplying exponents :

 6.1    5¹  multiplied by  5⁵   = 5^{(1 + 5)} = 5⁶

Dividing exponents :

 6.2    2⁴   divided by   2⁵   = 2^{(4 - 5)} = 2^(-1) = ¹/_2¹ = ¹/₂

Equation at the end of step  6  :

     1  
  —————— • 6020
  (56•2)

Step  7  :

Dividing exponents :

 7.1    2²   divided by   2¹   = 2^{(2 - 1)} = 2¹ = 2

Dividing exponents :

 7.2    5¹   divided by   5⁶   = 5^{(1 - 6)} = 5^(-5) = ¹/_5⁵

Final result :

   602           
  ———— = 0.19264 
  3125