Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-3" was replaced by "^(-3)". 1 more similar replacement(s)

(2): "5.5" was replaced by "(55/10)".

Step  1  :

 1.1     10 = 2•5

(10)^-3 = (2•5)^(-3) = (2)^(-3) • (5)^(-3)

Equation at the end of step  1  :

   55
  (—— • (10-7)) ÷ (5 • ((2)(-3)•(5)(-3)))
   10

Step  2  :

Raising to a Power :

 2.1    5¹   divided by   5³   = 5^{(1 - 3)} = 5^(-2) = ¹/_5²

Equation at the end of step  2  :

   55              1 
  (—— • (10-7)) ÷ ———
   10             200

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

   55                         1 
  (—— • ((2)(-7)•(5)(-7))) ÷ ———
   10                        200

Step  4  :

            11
 Simplify   ——
            2 

Equation at the end of step  4  :

  11                         1 
  —— • ((2)(-7)•(5)(-7))) ÷ ———
  2                         200

Step  5  :

Multiplying exponents :

 5.1    2¹  multiplied by  2⁷   = 2^{(1 + 7)} = 2⁸

Equation at the end of step  5  :

     11      1 
  ——————— ÷ ———
  (28•57)   200

Step  6  :

            11         1 
 Divide  ———————  by  ———
         (28•57)      200

 6.1    Dividing fractions

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

   11        1           11       200
———————  ÷  ———   =   ———————  •  ———
(28•57)     200       (28•57)      1 

Dividing exponents :

 6.2    2³   divided by   2⁸   = 2^{(3 - 8)} = 2^(-5) = ¹/_2⁵

Dividing exponents :

 6.3    5²   divided by   5⁷   = 5^{(2 - 7)} = 5^(-5) = ¹/_5⁵

Final result :

     11             
  ——————— = 0.00011 
  (25•55)