Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-5" was replaced by "^(-5)". 1 more similar replacement(s)

(2): "6.92" was replaced by "(692/100)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   8 692
  (—•———)•((2)(-5)•(5)(-5))
   1 100

Step  2  :

            173
 Simplify   ———
            25 

Equation at the end of step  2  :

   8   173
  (— • ———) • ((2)(-5)•(5)(-5))
   1   25 

Step  3  :

 3.1     10 = 2•5

(10)^-4 = (2•5)^(-4) = (2)^(-4) • (5)^(-4)

Equation at the end of step  3  :

   8   173
  (— • ———) • ((2)(-5)•(5)(-5))
   1   25 

Step  4  :

            1         173
 Divide  ———————  by  ———
         (24•54)      25 

 4.1    Dividing fractions

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

   1        173          1         25
———————  ÷  ———   =   ———————  •  ———
(24•54)     25        (24•54)     173

Dividing exponents :

 4.2    5²   divided by   5⁴   = 5^{(2 - 4)} = 5^(-2) = ¹/_5²

Equation at the end of step  4  :

   8        1     
  (— • ———————————) • ((2)(-5)•(5)(-5))
   1   (24•52•173)

Step  5  :

            8
 Simplify   —
            1

Equation at the end of step  5  :

            1     
  (8 • ———————————) • ((2)(-5)•(5)(-5))
       (24•52•173)

Step  6  :

Dividing exponents :

 6.1    2³   divided by   2⁴   = 2^{(3 - 4)} = 2^(-1) = ¹/_2¹ = ¹/₂

Equation at the end of step  6  :

    1 
  ———— • ((2)(-5)•(5)(-5))
  8650

Step  7  :

Multiplying exponents :

 7.1    2¹  multiplied by  2⁵   = 2^{(1 + 5)} = 2⁶

Multiplying exponents :

 7.2    5²  multiplied by  5⁵   = 5^{(2 + 5)} = 5⁷

Final result :

       1                                       
  ——————————— = 1.15607 • 10-9 
  (26•57•173)