Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-7" was replaced by "^(-7)".

(2): "7.2" was replaced by "(72/10)".

Step  1  :

 1.1     10 = 2•5

(10)^-7 = (2•5)^(-7) = (2)^(-7) • (5)^(-7)

Equation at the end of step  1  :

   72
  (—— • (106)) ÷ (3 • ((2)(-7)•(5)(-7)))
   10

Step  2  :

Equation at the end of step  2  :

   72               3   
  (—— • (106)) ÷ ———————
   10            (27•57)

Step  3  :

 3.1     10 = 2•5

(10)⁶ = (2•5)⁶ = 2⁶ • 5⁶

Equation at the end of step  3  :

   72                 3   
  (—— • (26•56)) ÷ ———————
   10              (27•57)

Step  4  :

            36
 Simplify   ——
            5 

Equation at the end of step  4  :

  36                 3   
  —— • (26•56)) ÷ ———————
  5               (27•57)

Step  5  :

Multiplying exponents :

 5.1    2²  multiplied by  2⁶   = 2^{(2 + 6)} = 2⁸

Dividing exponents :

 5.2    5⁶   divided by   5¹   = 5^{(6 - 1)} = 5⁵

Equation at the end of step  5  :

  5)3 
  ———————
  (27•57)

Step  6  :

                            3   
 Divide  (28•32•55)  by  ———————
                         (27•57)

Multiplying exponents :

 6.1    2⁸  multiplied by  2⁷   = 2^{(8 + 7)} = 2¹⁵

Multiplying exponents :

 6.2    5⁵  multiplied by  5⁷   = 5^{(5 + 7)} = 5¹²

Dividing exponents :

 6.3    3²   divided by   3¹   = 3^{(2 - 1)} = 3¹ = 3

Final result :

  (215•3•512)