Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-5" was replaced by "^(-5)". 1 more similar replacement(s)

(2): "2.32" was replaced by "(232/100)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   232
  (——— • (10-6)) • (4 • ((2)(-5)•(5)(-5)))
   100

Step  2  :

Raising to a Power :

 2.1    2²   divided by   2⁵   = 2^{(2 - 5)} = 2^(-3) = ¹/_2³

Equation at the end of step  2  :

   232                1   
  (——— • (10-6)) • ———————
   100             (23•55)

Step  3  :

 3.1     10 = 2•5

(10)^-6 = (2•5)^(-6) = (2)^(-6) • (5)^(-6)

Equation at the end of step  3  :

   232                           1   
  (——— • ((2)(-6)•(5)(-6))) • ———————
   100                        (23•55)

Step  4  :

            58
 Simplify   ——
            25

Equation at the end of step  4  :

   58                           1   
  (—— • ((2)(-6)•(5)(-6))) • ———————
   25                        (23•55)

Step  5  :

Multiplying exponents :

 5.1    5²  multiplied by  5⁶   = 5^{(2 + 6)} = 5⁸

Dividing exponents :

 5.2    2¹   divided by   2⁶   = 2^{(1 - 6)} = 2^(-5) = ¹/_2⁵

Equation at the end of step  5  :

     29        1   
  ——————— • ———————
  (58•25)   (23•55)

Step  6  :

Multiplying exponents :

 6.1    5⁸  multiplied by  5⁵   = 5^{(8 + 5)} = 5¹³

Multiplying exponents :

 6.2    2⁵  multiplied by  2³   = 2^{(5 + 3)} = 2⁸

Final result :

     29                                      
  ———————— = 9.28000 • 10-11 
  (513•28)