Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)⁸ = (2•5)⁸ = 2⁸ • 5⁸

Equation at the end of step  1  :

       (103)
  (3 • —————) • (28•58)
         6  

Step  2  :

 2.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  2  :

       (23•53)
  (3 • ———————) • (28•58)
          6   

Step  3  :

            (23•53)
 Simplify   ———————
               6   

Dividing exponents :

 3.1    2³   divided by   2¹   = 2^{(3 - 1)} = 2²

Equation at the end of step  3  :

       500
  (3 • ———) • (28•58)
        3 

Step  4  :

Multiplying exponents :

 4.1    2²  multiplied by  2⁸   = 2^{(2 + 8)} = 2¹⁰

Multiplying exponents :

 4.2    5³  multiplied by  5⁸   = 5^{(3 + 8)} = 5¹¹

Final result :

  (210•511)