Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)⁸ = (2•5)⁸ = 2⁸ • 5⁸

Equation at the end of step  1  :

       (1015)
  (7 • ——————) • (28•58)
         4   

Step  2  :

 2.1     10 = 2•5

(10)¹⁵ = (2•5)¹⁵ = 2¹⁵ • 5¹⁵

Equation at the end of step  2  :

       (215•515) 
  (7 • —————————) • (28•58)
           4    

Step  3  :

            (215•515) 
 Simplify   —————————
                4    

Dividing exponents :

 3.1    2¹⁵   divided by   2²   = 2^{(15 - 2)} = 2¹³

Equation at the end of step  3  :

  (7 • (213•515)) • (28•58)

Step  4  :

Equation at the end of step  4  :

  (7•213•515) • (28•58)

Step  5  :

Multiplying exponents :

 5.1    2¹³  multiplied by  2⁸   = 2^{(13 + 8)} = 2²¹

Multiplying exponents :

 5.2    5¹⁵  multiplied by  5⁸   = 5^{(15 + 8)} = 5²³

Final result :

  (7•221•523)