Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "6.8" was replaced by "(68/10)".

Step  1  :

 1.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  1  :

   68
  (—— • (109)) • (2 • (23•53))
   10

Step  2  :

Raising to a Power :

 2.1    2¹  multiplied by  2³   = 2^{(1 + 3)} = 2⁴

Equation at the end of step  2  :

   68
  (—— • (109)) • (24•53)
   10

Step  3  :

 3.1     10 = 2•5

(10)⁹ = (2•5)⁹ = 2⁹ • 5⁹

Equation at the end of step  3  :

   68
  (—— • (29•59)) • (24•53)
   10

Step  4  :

            34
 Simplify   ——
            5 

Equation at the end of step  4  :

   34
  (—— • (29•59)) • (24•53)
   5 

Step  5  :

Multiplying exponents :

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

Dividing exponents :

 5.2    5⁹   divided by   5¹   = 5^{(9 - 1)} = 5⁸

Equation at the end of step  5  :

  (210•17•58) • (24•53)

Step  6  :

Multiplying exponents :

 6.1    2¹⁰  multiplied by  2⁴   = 2^{(10 + 4)} = 2¹⁴

Multiplying exponents :

 6.2    5⁸  multiplied by  5³   = 5^{(8 + 3)} = 5¹¹

Final result :

  (214•17•511)