Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)⁶ = (2•5)⁶ = 2⁶ • 5⁶

Equation at the end of step  1  :

Step  2  :

Raising to a Power :

 2.1    2¹  multiplied by  2⁶   = 2^{(1 + 6)} = 2⁷

Equation at the end of step  2  :

Step  3  :

 3.1     10 = 2•5

(10)¹² = (2•5)¹² = 2¹² • 5¹²

Equation at the end of step  3  :

Step  4  :

Multiplying exponents :

 4.1    5¹  multiplied by  5¹²   = 5^{(1 + 12)} = 5¹³

Equation at the end of step  4  :

Step  5  :

            (513•212)
 Simplify   —————————
             (27•56) 

Dividing exponents :

 5.1    5¹³   divided by   5⁶   = 5^{(13 - 6)} = 5⁷

Dividing exponents :

 5.2    2¹²   divided by   2⁷   = 2^{(12 - 7)} = 2⁵

Final result :

  (57•25)