Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "3.6" was replaced by "(36/10)". 2 more similar replacement(s)

Step  1  :

 1.1     70 = 2•5•7

(70)³ = (2•5•7)³ = 2³ • 5³ • 7³

Equation at the end of step  1  :

   741       36
  {———}6 • ({——}(2^3•5^3•7^3)
   100       10

Step  2  :

            18
 Simplify   ——
            5 

Equation at the end of step  2  :

   741      18
  {———}6 • (——)(2^3•5^3•7^3))
   100      5 

Step  3  :

 3.1     18 = 2•32

(18)³⁴³⁰⁰⁰ = (2•3²)³⁴³⁰⁰⁰ = 2³⁴³⁰⁰⁰ • 3⁶⁸⁶⁰⁰⁰

Equation at the end of step  3  :

   741     (2343000•3686000) 
  {———}6 • —————————————————
   100          5343000     

Step  4  :

            741
 Simplify   ———
            100

Equation at the end of step  4  :

   741      (2343000•3686000) 
  (———)6) • —————————————————
   100           5343000     

Step  5  :

 5.1     741 = 3•13•19

(741)⁶ = (3•13•19)⁶ = 3⁶ • 13⁶ • 19⁶  5.2     100 = 2²•5² (100)⁶ = (2²•5²)⁶ = 2¹² • 5¹²

Equation at the end of step  5  :

  (36•136•196)   (2343000•3686000) 
  ———————————— • —————————————————
   (212•512)          5343000     

Step  6  :

Multiplying exponents :

 6.1    3⁶  multiplied by  3⁶⁸⁶⁰⁰⁰   = 3^{(6 + 686000)} = 3⁶⁸⁶⁰⁰⁶

Multiplying exponents :

 6.2    5¹²  multiplied by  5³⁴³⁰⁰⁰   = 5^{(12 + 343000)} = 5³⁴³⁰¹²

Dividing exponents :

 6.3    2³⁴³⁰⁰⁰   divided by   2¹²   = 2^{(343000 - 12)} = 2³⁴²⁹⁸⁸

Final result :

  (3686006•136•196•2342988)                                       
  ————————————————————————— = 9.47703 • 10190816 
           5343012