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    2¹  multiplied by  2⁵   = 2^{(1 + 5)} = 2⁶

Equation at the end of step  2  :

Step  3  :

 3.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  3  :

Step  4  :

Multiplying exponents :

 4.1    2³  multiplied by  2³   = 2^{(3 + 3)} = 2⁶

Equation at the end of step  4  :

Step  5  :

            (26•53)
 Simplify   ———————
            (26•55)

Canceling Out :

 5.1      Canceling out  2⁶ as it appears on both sides of the fraction line

Dividing exponents :

 5.2    5³   divided by   5⁵   = 5^{(3 - 5)} = 5^(-2) = ¹/_5²

Final result :

   1           
  —— = 0.04000 
  25