Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-7" was replaced by "^(-7))". 1 more similar replacement(s)

(2): "6.45" was replaced by "(645/100)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   663 645
  (———•———)•((2)(-7)•(5)(-7))
   100 100

Step  2  :

            129
 Simplify   ———
            20 

Equation at the end of step  2  :

   663   129
  (——— • ———) • ((2)(-7)•(5)(-7))
   100   20 

Step  3  :

 3.1     10 = 2•5

(10)^-34 = (2•5)^(-34) = (2)^(-34) • (5)^(-34)

Equation at the end of step  3  :

   663   129
  (——— • ———) • ((2)(-7)•(5)(-7))
   100   20 

Step  4  :

             1          129
 Divide  —————————  by  ———
         (234•534)       20 

 4.1    Dividing fractions

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

    1         129           1          20
—————————  ÷  ———   =   —————————  •  ———
(234•534)      20        (234•534)      129

Dividing exponents :

 4.2    2²   divided by   2³⁴   = 2^{(2 - 34)} = 2^(-32) = ¹/_2³²

Dividing exponents :

 4.3    5¹   divided by   5³⁴   = 5^{(1 - 34)} = 5^(-33) = ¹/_5³³

Equation at the end of step  4  :

   663          1      
  (——— • ——————————————) • ((2)(-7)•(5)(-7))
   100   (232•533•3•43) 

Step  5  :

            663
 Simplify   ———
            100

Equation at the end of step  5  :

   663          1      
  (——— • ——————————————) • ((2)(-7)•(5)(-7))
   100   (232•533•3•43) 

Step  6  :

Multiplying exponents :

 6.1    2²  multiplied by  2³²   = 2^{(2 + 32)} = 2³⁴

Multiplying exponents :

 6.2    5²  multiplied by  5³³   = 5^{(2 + 33)} = 5³⁵

Canceling Out :

 6.3      Canceling out  3  as it appears on both sides of the fraction line

Equation at the end of step  6  :

       221    
  ———————————— • ((2)(-7)•(5)(-7))
  (234•535•43) 

Step  7  :

Multiplying exponents :

 7.1    2³⁴  multiplied by  2⁷   = 2^{(34 + 7)} = 2⁴¹

Multiplying exponents :

 7.2    5³⁵  multiplied by  5⁷   = 5^{(35 + 7)} = 5⁴²

Final result :

       221                                       
  ———————————— = 1.02791 • 10-41 
  (241•542•43)