Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-8" was replaced by "^(-8))". 1 more similar replacement(s)

(2): "6.31" was replaced by "(631/100)".

Step  1  :

 1.1     10 = 2•5

(10)^-8 = (2•5)^(-8) = (2)^(-8) • (5)^(-8)

Equation at the end of step  1  :

       631
  (1 • ———) • ((2)(-8)•(5)(-8))
       100

Step  2  :

            631
 Simplify   ———
            100

Equation at the end of step  2  :

       631
  (1 • ———) • ((2)(-8)•(5)(-8))
       100

Step  3  :

 3.1     10 = 2•5

(10)^-14 = (2•5)^(-14) = (2)^(-14) • (5)^(-14)

Equation at the end of step  3  :

       631
  (1 • ———) • ((2)(-8)•(5)(-8))
       100

Step  4  :

             1          631
 Divide  —————————  by  ———
         (214•514)       100

 4.1    Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

    1         631           1         100
—————————  ÷  ———   =   —————————  •  ———
(214•514)      100       (214•514)      631

Dividing exponents :

 4.2    2²   divided by   2¹⁴   = 2^{(2 - 14)} = 2^(-12) = ¹/_2¹²

Dividing exponents :

 4.3    5²   divided by   5¹⁴   = 5^{(2 - 14)} = 5^(-12) = ¹/_5¹²

Equation at the end of step  4  :

             1      
  (1 • —————————————) • ((2)(-8)•(5)(-8))
       (212•512•631) 

Step  5  :

Multiplying exponents :

 5.1    2¹²  multiplied by  2⁸   = 2^{(12 + 8)} = 2²⁰

Multiplying exponents :

 5.2    5¹²  multiplied by  5⁸   = 5^{(12 + 8)} = 5²⁰

Final result :

        1                                         
  ————————————— = 1.58479 • 10-23 
  (220•520•631)