Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  1  :

Step  2  :

Raising to a Power :

 2.1    2²  multiplied by  2⁵   = 2^{(2 + 5)} = 2⁷

Equation at the end of step  2  :

Step  3  :

 3.1     10 = 2•5

(10)¹¹ = (2•5)¹¹ = 2¹¹ • 5¹¹

Equation at the end of step  3  :

Step  4  :

Multiplying exponents :

 4.1    2³  multiplied by  2¹¹   = 2^{(3 + 11)} = 2¹⁴

Equation at the end of step  4  :

Step  5  :

            (214•511)
 Simplify   —————————
             (27•55) 

Dividing exponents :

 5.1    2¹⁴   divided by   2⁷   = 2^{(14 - 7)} = 2⁷

Dividing exponents :

 5.2    5¹¹   divided by   5⁵   = 5^{(11 - 5)} = 5⁶

Final result :

  (27•56)