Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)⁹ = (2•5)⁹ = 2⁹ • 5⁹

Equation at the end of step  1  :

  (104)
  ————— • (29•59)
  (103)

Step  2  :

 2.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  2  :

   (104) 
  ——————— • (29•59)
  (23•53)

Step  3  :

 3.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  3  :

  (24•54)
  ——————— • (29•59)
  (23•53)

Step  4  :

            (24•54)
 Simplify   ———————
            (23•53)

Dividing exponents :

 4.1    2⁴   divided by   2³   = 2^{(4 - 3)} = 2¹ = 2

Dividing exponents :

 4.2    5⁴   divided by   5³   = 5^{(4 - 3)} = 5¹ = 5

Equation at the end of step  4  :

  10 • (29•59)

Step  5  :

Multiplying exponents :

 5.1    2¹  multiplied by  2⁹   = 2^{(1 + 9)} = 2¹⁰

Multiplying exponents :

 5.2    5¹  multiplied by  5⁹   = 5^{(1 + 9)} = 5¹⁰

Final result :

  (210•510)