Solution - Power equations

Step  1  :

Equation at the end of step  1  :

        (2•(103))
  ((54)+—————————)-5
           400   

Step  2  :

 2.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  2  :

           (2 • (23•53))     
  ((54) +  —————————————) -  5
                400          

Step  3  :

Multiplying exponents :

 3.1    2¹  multiplied by  2³   = 2^{(1 + 3)} = 2⁴

Equation at the end of step  3  :

           (24•53)     
  ((54) +  ———————) -  5
             400       

Step  4  :

            (24•53)
 Simplify   ———————
              400  

Canceling Out :

 4.1      Canceling out  2⁴ as it appears on both sides of the fraction line

Dividing exponents :

 4.2    5³   divided by   5²   = 5^{(3 - 2)} = 5¹ = 5

Equation at the end of step  4  :

  ((54) +  5) -  5

Step  5  :

Equation at the end of step  5  :

  (54 +  5) -  5

Step  6  :

Final result :

  625