Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-3" was replaced by "^(-3)".

(2): "2.5" was replaced by "(25/10)". 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  :

   28         25
  (——•(107))•(——•((2)(-3)•(5)(-3)))
   10         10

Step  2  :

            5
 Simplify   —
            2

Equation at the end of step  2  :

   28             5
  (—— • (107)) • (— • ((2)(-3)•(5)(-3)))
   10             2

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2³   = 2^{(1 + 3)} = 2⁴

Raising to a Power :

 3.2    5¹   divided by   5³   = 5^{(1 - 3)} = 5^(-2) = ¹/_5²

Equation at the end of step  3  :

   28             1 
  (—— • (107)) • ———
   10            400

Step  4  :

 4.1     10 = 2•5

(10)⁷ = (2•5)⁷ = 2⁷ • 5⁷

Equation at the end of step  4  :

   28               1 
  (—— • (27•57)) • ———
   10              400

Step  5  :

            14
 Simplify   ——
            5 

Equation at the end of step  5  :

   14               1 
  (—— • (27•57)) • ———
   5               400

Step  6  :

Multiplying exponents :

 6.1    2¹  multiplied by  2⁷   = 2^{(1 + 7)} = 2⁸

Dividing exponents :

 6.2    5⁷   divided by   5¹   = 5^{(7 - 1)} = 5⁶

Equation at the end of step  6  :

               1 
  (28•7•56) • ———
              400

Step  7  :

Dividing exponents :

 7.1    2⁸   divided by   2⁴   = 2^{(8 - 4)} = 2⁴

Dividing exponents :

 7.2    5⁶   divided by   5²   = 5^{(6 - 2)} = 5⁴

Final result :

  (24•7•54)