Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)⁹ = (2•5)⁹ = 2⁹ • 5⁹

Equation at the end of step  1  :

Step  2  :

Raising to a Power :

 2.1    2¹  multiplied by  2⁹   = 2^{(1 + 9)} = 2¹⁰

Equation at the end of step  2  :

Step  3  :

 3.1     10 = 2•5

(10)²⁰ = (2•5)²⁰ = 2²⁰ • 5²⁰

Equation at the end of step  3  :

Step  4  :

Multiplying exponents :

 4.1    2³  multiplied by  2²⁰   = 2^{(3 + 20)} = 2²³

Equation at the end of step  4  :

Step  5  :

             (223•520)
 Simplify   ——————————
            (210•3•59)

Dividing exponents :

 5.1    2²³   divided by   2¹⁰   = 2^{(23 - 10)} = 2¹³

Dividing exponents :

 5.2    5²⁰   divided by   5⁹   = 5^{(20 - 9)} = 5¹¹

Final result :

  (213•511)                                   
  ————————— = 1.33333 • 1011 
      3