Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.3" was replaced by "(13/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)⁷ = (2•5)⁷ = 2⁷ • 5⁷

Equation at the end of step  1  :

   52        13
  (——•(1013))——•(27•57))
   10(       10

Step  2  :

            13
 Simplify   ——
            10

Equation at the end of step  2  :

   52              13
  (—— • (1013)) ÷ (—— • (27•57))
   10              10

Step  3  :

Dividing exponents :

 3.1    2⁷   divided by   2¹   = 2^{(7 - 1)} = 2⁶

Raising to a Power :

 3.2    5⁷   divided by   5¹   = 5^{(7 - 1)} = 5⁶

Equation at the end of step  3  :

   52
  (—— • (1013)) ÷ (13•26•56)
   10

Step  4  :

 4.1     10 = 2•5

(10)¹³ = (2•5)¹³ = 2¹³ • 5¹³

Equation at the end of step  4  :

   52
  (—— • (213•513)) ÷ (13•26•56)
   10

Step  5  :

            26
 Simplify   ——
            5 

Equation at the end of step  5  :

  26
  —— • (213•513)) ÷ (13•26•56)
  5 

Step  6  :

Multiplying exponents :

 6.1    2¹  multiplied by  2¹³   = 2^{(1 + 13)} = 2¹⁴

Dividing exponents :

 6.2    5¹³   divided by   5¹   = 5^{(13 - 1)} = 5¹²

Equation at the end of step  6  :

Step  7  :

            (214•13•512)
 Simplify   ————————————
             (13•26•56) 

Dividing exponents :

 7.1    2¹⁴   divided by   2⁶   = 2^{(14 - 6)} = 2⁸

Canceling Out :

 7.2      Canceling out  13  as it appears on both sides of the fraction line

Dividing exponents :

 7.3    5¹²   divided by   5⁶   = 5^{(12 - 6)} = 5⁶

Final result :

  (28•56)