Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)⁷ = (2•5)⁷ = 2⁷ • 5⁷

Equation at the end of step  1  :

Step  2  :

Raising to a Power :

 2.1    2¹  multiplied by  2⁷   = 2^{(1 + 7)} = 2⁸

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    2²  multiplied by  2⁶   = 2^{(2 + 6)} = 2⁸

Equation at the end of step  4  :

Step  5  :

            (28•56)
 Simplify   ———————
            (28•57)

Canceling Out :

 5.1      Canceling out  2⁸ as it appears on both sides of the fraction line

Dividing exponents :

 5.2    5⁶   divided by   5⁷   = 5^{(6 - 7)} = 5^(-1) = ¹/_5¹ = ¹/₅

Final result :

  1           
  — = 0.20000 
  5