Solution - Power equations

Step  1  :

 1.1     6 = 2•3

(6)⁵ = (2•3)⁵ = 2⁵ • 3⁵

Equation at the end of step  1  :

Step  2  :

 2.1     35 = 5•7

(35)⁶ = (5•7)⁶ = 5⁶ • 7⁶

Equation at the end of step  2  :

Step  3  :

 3.1     15 = 3•5

(15)⁵ = (3•5)⁵ = 3⁵ • 5⁵

Equation at the end of step  3  :

Step  4  :

 4.1     14 = 2•7

(14)⁶ = (2•7)⁶ = 2⁶ • 7⁶

Equation at the end of step  4  :

Step  5  :

            (26•76•35•55)
 Simplify   —————————————
            (56•76•25•35)

Dividing exponents :

 5.1    2⁶   divided by   2⁵   = 2^{(6 - 5)} = 2¹ = 2

Canceling Out :

 5.2      Canceling out  7⁶ as it appears on both sides of the fraction line

Canceling Out :

 5.3      Canceling out  3⁵ as it appears on both sides of the fraction line

Dividing exponents :

 5.4    5⁵   divided by   5⁶   = 5^{(5 - 6)} = 5^(-1) = ¹/_5¹ = ¹/₅

Final result :

  2           
  — = 0.40000 
  5