Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-9" was replaced by "^(-9)".

(2): "1.6" was replaced by "(16/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)^-9 = (2•5)^(-9) = (2)^(-9) • (5)^(-9)

Equation at the end of step  1  :

   72        16
  (——•(1011))——•((2)(-9)•(5)(-9)))
   10(       10

Step  2  :

            8
 Simplify   —
            5

Equation at the end of step  2  :

   72              8
  (—— • (1011)) ÷ (— • ((2)(-9)•(5)(-9)))
   10              5

Step  3  :

Multiplying exponents :

 3.1    5¹  multiplied by  5⁹   = 5^{(1 + 9)} = 5¹⁰

Raising to a Power :

 3.2    2³   divided by   2⁹   = 2^{(3 - 9)} = 2^(-6) = ¹/_2⁶

Equation at the end of step  3  :

   72                 1   
  (—— • (1011)) ÷ ————————
   10             (510•26) 

Step  4  :

 4.1     10 = 2•5

(10)¹¹ = (2•5)¹¹ = 2¹¹ • 5¹¹

Equation at the end of step  4  :

   72                    1   
  (—— • (211•511)) ÷ ————————
   10                (510•26) 

Step  5  :

            36
 Simplify   ——
            5 

Equation at the end of step  5  :

  36                    1   
  —— • (211•511)) ÷ ————————
  5                 (510•26) 

Step  6  :

Multiplying exponents :

 6.1    2²  multiplied by  2¹¹   = 2^{(2 + 11)} = 2¹³

Dividing exponents :

 6.2    5¹¹   divided by   5¹   = 5^{(11 - 1)} = 5¹⁰

Equation at the end of step  6  :

  10)1 
  ————————
  (510•26)

Step  7  :

                               1   
 Divide  (213•32•510)  by  ————————
                           (510•26) 

Multiplying exponents :

 7.1    2¹³  multiplied by  2⁶   = 2^{(13 + 6)} = 2¹⁹

Multiplying exponents :

 7.2    5¹⁰  multiplied by  5¹⁰   = 5^{(10 + 10)} = 5²⁰

Final result :

  (219•32•520)