Solution - Power equations

Step  1  :

 1.1     10 = 2•5

(10)²⁶ = (2•5)²⁶ = 2²⁶ • 5²⁶

Equation at the end of step  1  :

Step  2  :

Raising to a Power :

 2.1    2¹  multiplied by  2²⁶   = 2^{(1 + 26)} = 2²⁷

Equation at the end of step  2  :

Step  3  :

 3.1     10 = 2•5

(10)¹⁶ = (2•5)¹⁶ = 2¹⁶ • 5¹⁶

Equation at the end of step  3  :

Step  4  :

Multiplying exponents :

 4.1    2⁴  multiplied by  2¹⁶   = 2^{(4 + 16)} = 2²⁰

Equation at the end of step  4  :

Step  5  :

            (220•516)
 Simplify   —————————
            (227•526)

Dividing exponents :

 5.1    2²⁰   divided by   2²⁷   = 2^{(20 - 27)} = 2^(-7) = ¹/_2⁷

Dividing exponents :

 5.2    5¹⁶   divided by   5²⁶   = 5^{(16 - 26)} = 5^(-10) = ¹/_5¹⁰

Final result :

      1                                      
  ———————— = 8.00000 • 10-10 
  (27•510)