Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-7" was replaced by "^(-7)".

(2): ".4" was replaced by "(4/10)". 3 more similar replacement(s)

Step  1  :

            2
 Simplify   —
            5

Equation at the end of step  1  :

   362    21         2
  ———— ÷ ———•((10-7)•—)
  1000   100         5

Step  2  :

 2.1     10 = 2•5

(10)^-7 = (2•5)^(-7) = (2)^(-7) • (5)^(-7)

Equation at the end of step  2  :

   362    21                        2
  ———— ÷ ——— • (((2)(-7)•(5)(-7)) • —)
  1000   100                        5

Step  3  :

Multiplying exponents :

 3.1    5⁷  multiplied by  5¹   = 5^{(7 + 1)} = 5⁸

Dividing exponents :

 3.2    2¹   divided by   2⁷   = 2^{(1 - 7)} = 2^(-6) = ¹/_2⁶

Equation at the end of step  3  :

   362    21      1   
  ———— ÷ ——— • ———————
  1000   100   (26•58)

Step  4  :

             21
 Simplify   ———
            100

Equation at the end of step  4  :

   362    21      1   
  ———— ÷ ——— • ———————
  1000   100   (26•58)

Step  5  :

            181
 Simplify   ———
            500

Equation at the end of step  5  :

  181    21      1   
  ——— ÷ ——— • ———————
  500   100   (26•58)

Step  6  :

         181       21
 Divide  ———  by  ———
         500      100

 6.1    Dividing fractions

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

181      21       181     100
———  ÷  ———   =   ———  •  ———
500     100       500     21 

Equation at the end of step  6  :

  181      1   
  ——— • ———————
  105   (26•58)

Step  7  :

Multiplying exponents :

 7.1    5¹  multiplied by  5⁸   = 5^{(1 + 8)} = 5⁹

Final result :

      181                                      
  ——————————— = 6.89524 • 10-8 
  (3•59•7•26)