Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "2.3" was replaced by "(23/10)". 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  :

   69       23
  (——•(107))——•((2)(-3)•(5)(-3)))
   10(      10

Step  2  :

            23
 Simplify   ——
            10

Equation at the end of step  2  :

   69             23
  (—— • (107)) ÷ (—— • ((2)(-3)•(5)(-3)))
   10             10

Step  3  :

Multiplying exponents :

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

Raising to a Power :

 3.2    5¹  multiplied by  5³   = 5^{(1 + 3)} = 5⁴

Equation at the end of step  3  :

   69               23  
  (—— • (107)) ÷ ———————
   10            (24•54)

Step  4  :

 4.1     10 = 2•5

(10)⁷ = (2•5)⁷ = 2⁷ • 5⁷

Equation at the end of step  4  :

   69                 23  
  (—— • (27•57)) ÷ ———————
   10              (24•54)

Step  5  :

            69
 Simplify   ——
            10

Equation at the end of step  5  :

  69                 23  
  —— • (27•57)) ÷ ———————
  10              (24•54)

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  :

  6)23 
  ———————
  (24•54)

Step  7  :

                              23  
 Divide  (3•23•26•56)  by  ———————
                           (24•54)

Multiplying exponents :

 7.1    2⁶  multiplied by  2⁴   = 2^{(6 + 4)} = 2¹⁰

Multiplying exponents :

 7.2    5⁶  multiplied by  5⁴   = 5^{(6 + 4)} = 5¹⁰

Canceling Out :

 7.3      Canceling out  23  as it appears on both sides of the fraction line

Final result :

  (3•210•510)