Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

  (4 • (103)) • (6 • ((2)(-5)•(5)(-5)))

Step  2  :

Raising to a Power :

 2.1    2¹   divided by   2⁵   = 2^{(1 - 5)} = 2^(-4) = ¹/_2⁴

Equation at the end of step  2  :

                   3   
  (4 • (103)) • ———————
                (24•55)

Step  3  :

 3.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  3  :

                     3   
  (4 • (23•53)) • ———————
                  (24•55)

Step  4  :

Multiplying exponents :

 4.1    2²  multiplied by  2³   = 2^{(2 + 3)} = 2⁵

Equation at the end of step  4  :

               3   
  (25•53) • ———————
            (24•55)

Step  5  :

Dividing exponents :

 5.1    2⁵   divided by   2⁴   = 2^{(5 - 4)} = 2¹ = 2

Dividing exponents :

 5.2    5³   divided by   5⁵   = 5^{(3 - 5)} = 5^(-2) = ¹/_5²

Final result :

   6           
  —— = 0.24000 
  25