Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-3" was replaced by "^(-3)". 1 more similar replacement(s)

(2): "1.2" was replaced by "(12/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)^-3 = (2•5)^(-3) = (2)^(-3) • (5)^(-3)

Equation at the end of step  1  :

   38          12
  (——•(10-9))•(——•((2)(-3)•(5)(-3)))
   10          10

Step  2  :

            6
 Simplify   —
            5

Equation at the end of step  2  :

   38              6
  (—— • (10-9)) • (— • ((2)(-3)•(5)(-3)))
   10              5

Step  3  :

Multiplying exponents :

 3.1    5¹  multiplied by  5³   = 5^{(1 + 3)} = 5⁴

Raising to a Power :

 3.2    2¹   divided by   2³   = 2^{(1 - 3)} = 2^(-2) = ¹/_2²

Equation at the end of step  3  :

   38               3 
  (—— • (10-9)) • ————
   10             2500

Step  4  :

 4.1     10 = 2•5

(10)^-9 = (2•5)^(-9) = (2)^(-9) • (5)^(-9)

Equation at the end of step  4  :

   38                          3 
  (—— • ((2)(-9)•(5)(-9))) • ————
   10                        2500

Step  5  :

            19
 Simplify   ——
            5 

Equation at the end of step  5  :

   19                          3 
  (—— • ((2)(-9)•(5)(-9))) • ————
   5                         2500

Step  6  :

Multiplying exponents :

 6.1    5¹  multiplied by  5⁹   = 5^{(1 + 9)} = 5¹⁰

Equation at the end of step  6  :

     19        3 
  ———————— • ————
  (510•29)    2500

Step  7  :

Multiplying exponents :

 7.1    5¹⁰  multiplied by  5⁴   = 5^{(10 + 4)} = 5¹⁴

Multiplying exponents :

 7.2    2⁹  multiplied by  2²   = 2^{(9 + 2)} = 2¹¹

Final result :

      57                                      
  ————————— = 4.56000 • 10-12 
  (514•211)