Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-4" was replaced by "^(-4)".

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

Step  1  :

 1.1     10 = 2•5

(10)^-4 = (2•5)^(-4) = (2)^(-4) • (5)^(-4)

Equation at the end of step  1  :

   96       12
  (——•(107))——•((2)(-4)•(5)(-4)))
   10(      10

Step  2  :

            6
 Simplify   —
            5

Equation at the end of step  2  :

   96             6
  (—— • (107)) ÷ (— • ((2)(-4)•(5)(-4)))
   10             5

Step  3  :

Multiplying exponents :

 3.1    5¹  multiplied by  5⁴   = 5^{(1 + 4)} = 5⁵

Raising to a Power :

 3.2    2¹   divided by   2⁴   = 2^{(1 - 4)} = 2^(-3) = ¹/_2³

Equation at the end of step  3  :

   96               3   
  (—— • (107)) ÷ ———————
   10            (55•23)

Step  4  :

 4.1     10 = 2•5

(10)⁷ = (2•5)⁷ = 2⁷ • 5⁷

Equation at the end of step  4  :

   96                 3   
  (—— • (27•57)) ÷ ———————
   10              (55•23)

Step  5  :

            48
 Simplify   ——
            5 

Equation at the end of step  5  :

  48                 3   
  —— • (27•57)) ÷ ———————
  5               (55•23)

Step  6  :

Multiplying exponents :

 6.1    2⁴  multiplied by  2⁷   = 2^{(4 + 7)} = 2¹¹

Dividing exponents :

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

Equation at the end of step  6  :

  6)3 
  ———————
  (55•23)

Step  7  :

                            3   
 Divide  (211•3•56)  by  ———————
                         (55•23)

Multiplying exponents :

 7.1    2¹¹  multiplied by  2³   = 2^{(11 + 3)} = 2¹⁴

Multiplying exponents :

 7.2    5⁶  multiplied by  5⁵   = 5^{(6 + 5)} = 5¹¹

Canceling Out :

 7.3      Canceling out  3  as it appears on both sides of the fraction line

Final result :

  (214•511)