Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  1  :

Step  2  :

Raising to a Power :

 2.1    2¹  multiplied by  2³   = 2^{(1 + 3)} = 2⁴

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    2²  multiplied by  2¹²   = 2^{(2 + 12)} = 2¹⁴

Equation at the end of step  4  :

Step  5  :

            (214•512)
 Simplify   —————————
             (24•53) 

Dividing exponents :

 5.1    2¹⁴   divided by   2⁴   = 2^{(14 - 4)} = 2¹⁰

Dividing exponents :

 5.2    5¹²   divided by   5³   = 5^{(12 - 3)} = 5⁹

Final result :

  (210•59)