Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.2" was replaced by "(42/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  1  :

   714       42
  (———•(107))——•(23•53))
   100(      10

Step  2  :

            21
 Simplify   ——
            5 

Equation at the end of step  2  :

   714             21
  (——— • (107)) ÷ (—— • (23•53))
   100             5 

Step  3  :

Raising to a Power :

 3.1    5³   divided by   5¹   = 5^{(3 - 1)} = 5²

Equation at the end of step  3  :

   714
  (——— • (107)) ÷ 4200
   100

Step  4  :

 4.1     10 = 2•5

(10)⁷ = (2•5)⁷ = 2⁷ • 5⁷

Equation at the end of step  4  :

   714
  (——— • (27•57)) ÷ 4200
   100

Step  5  :

            357
 Simplify   ———
            50 

Equation at the end of step  5  :

  357
  ——— • (27•57)) ÷ 4200
  50 

Step  6  :

Dividing exponents :

 6.1    2⁷   divided by   2¹   = 2^{(7 - 1)} = 2⁶

Dividing exponents :

 6.2    5⁷   divided by   5²   = 5^{(7 - 2)} = 5⁵

Equation at the end of step  6  :

Step  7  :

            (3•7•17•26•55)
 Simplify   ——————————————
                 4200     

Canceling Out :

 7.1      Canceling out  3  as it appears on both sides of the fraction line

Canceling Out :

 7.2      Canceling out  7  as it appears on both sides of the fraction line

Dividing exponents :

 7.3    2⁶   divided by   2³   = 2^{(6 - 3)} = 2³

Dividing exponents :

 7.4    5⁵   divided by   5²   = 5^{(5 - 2)} = 5³

Final result :

  (17•23•53)