Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "2.8" was replaced by "(28/10)". 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  :

   97         28
  (——•(107))•(——•((2)(-3)•(5)(-3)))
   10         10

Step  2  :

            14
 Simplify   ——
            5 

Equation at the end of step  2  :

   97             14
  (—— • (107)) • (—— • ((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  :

   97              7 
  (—— • (107)) • ————
   10            2500

Step  4  :

 4.1     10 = 2•5

(10)⁷ = (2•5)⁷ = 2⁷ • 5⁷

Equation at the end of step  4  :

   97                7 
  (—— • (27•57)) • ————
   10              2500

Step  5  :

            97
 Simplify   ——
            10

Equation at the end of step  5  :

   97                7 
  (—— • (27•57)) • ————
   10              2500

Step  6  :

Dividing exponents :

 6.1    2⁷   divided by   2¹   = 2^{(7 - 1)} = 2⁶

Dividing exponents :

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

Equation at the end of step  6  :

                 7 
  (97•26•56) • ————
               2500

Step  7  :

Dividing exponents :

 7.1    2⁶   divided by   2²   = 2^{(6 - 2)} = 2⁴

Dividing exponents :

 7.2    5⁶   divided by   5⁴   = 5^{(6 - 4)} = 5²

Final result :

  (97•24•52•7)