Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "7.2" was replaced by "(72/10)".

Step  1  :

 1.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  1  :

   72
  (—— • (105)) • (23•53)
   10

Step  2  :

 2.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  2  :

   72
  (—— • (25•55)) • (23•53)
   10

Step  3  :

            36
 Simplify   ——
            5 

Equation at the end of step  3  :

   36
  (—— • (25•55)) • (23•53)
   5 

Step  4  :

Multiplying exponents :

 4.1    2²  multiplied by  2⁵   = 2^{(2 + 5)} = 2⁷

Dividing exponents :

 4.2    5⁵   divided by   5¹   = 5^{(5 - 1)} = 5⁴

Equation at the end of step  4  :

  (27•32•54) • (23•53)

Step  5  :

Multiplying exponents :

 5.1    2⁷  multiplied by  2³   = 2^{(7 + 3)} = 2¹⁰

Multiplying exponents :

 5.2    5⁴  multiplied by  5³   = 5^{(4 + 3)} = 5⁷

Final result :

  (210•32•57)