Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  1  :

Step  2  :

Raising to a Power :

 2.1    2¹  multiplied by  2⁴   = 2^{(1 + 4)} = 2⁵

Equation at the end of step  2  :

Step  3  :

 3.1     10 = 2•5

(10)⁹ = (2•5)⁹ = 2⁹ • 5⁹

Equation at the end of step  3  :

Step  4  :

Multiplying exponents :

 4.1    2³  multiplied by  2⁹   = 2^{(3 + 9)} = 2¹²

Equation at the end of step  4  :

Step  5  :

            (212•59)
 Simplify   ————————
            (25•54) 

Dividing exponents :

 5.1    2¹²   divided by   2⁵   = 2^{(12 - 5)} = 2⁷

Dividing exponents :

 5.2    5⁹   divided by   5⁴   = 5^{(9 - 4)} = 5⁵

Final result :

  (27•55)