Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  1  :

Step  2  :

Raising to a Power :

 2.1    2¹  multiplied by  2²   = 2^{(1 + 2)} = 2³

Equation at the end of step  2  :

Step  3  :

 3.1     10 = 2•5

(10)⁶ = (2•5)⁶ = 2⁶ • 5⁶

Equation at the end of step  3  :

Step  4  :

Multiplying exponents :

 4.1    5¹  multiplied by  5⁶   = 5^{(1 + 6)} = 5⁷

Equation at the end of step  4  :

Step  5  :

             (57•26) 
 Simplify   —————————
            (23•3•52)

Dividing exponents :

 5.1    5⁷   divided by   5²   = 5^{(7 - 2)} = 5⁵

Dividing exponents :

 5.2    2⁶   divided by   2³   = 2^{(6 - 3)} = 2³

Final result :

  (55•23)              
  ——————— = 8333.33333 
     3