Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-21" was replaced by "^(-21)".

(2): "0.0424" was replaced by "(0424/10000)". 2 more similar replacement(s)

Step  1  :

             53 
 Simplify   ————
            1250

Equation at the end of step  1  :

   625               53 
  (——— • (10-21)) ÷ ————
   100              1250

Step  2  :

 2.1     10 = 2•5

(10)^-21 = (2•5)^(-21) = (2)^(-21) • (5)^(-21)

Equation at the end of step  2  :

   625                           53 
  (——— • ((2)(-21)•(5)(-21))) ÷ ————
   100                          1250

Step  3  :

            25
 Simplify   ——
            4 

Equation at the end of step  3  :

  25                           53 
  —— • ((2)(-21)•(5)(-21))) ÷ ————
  4                           1250

Step  4  :

Multiplying exponents :

 4.1    2²  multiplied by  2²¹   = 2^{(2 + 21)} = 2²³

Dividing exponents :

 4.2    5²   divided by   5²¹   = 5^{(2 - 21)} = 5^(-19) = ¹/_5¹⁹

Equation at the end of step  4  :

      1        53 
  ————————— ÷ ————
  (223•519)    1250

Step  5  :

             1           53 
 Divide  —————————  by  ————
         (223•519)       1250

 5.1    Dividing fractions

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

    1          53            1         1250
—————————  ÷  ————   =   —————————  •  ————
(223•519)      1250       (223•519)       53 

Dividing exponents :

 5.2    2¹   divided by   2²³   = 2^{(1 - 23)} = 2^(-22) = ¹/_2²²

Dividing exponents :

 5.3    5⁴   divided by   5¹⁹   = 5^{(4 - 19)} = 5^(-15) = ¹/_5¹⁵

Final result :

        1                                        
  ———————————— = 1.47406 • 10-19 
  (222•515•53)