Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-8" was replaced by "^(-8)". 1 more similar replacement(s)

(2): "3.5" was replaced by "(35/10)".

Step  1  :

 1.1     10 = 2•5

(10)^-8 = (2•5)^(-8) = (2)^(-8) • (5)^(-8)

Equation at the end of step  1  :

   35
  (—— • (10-4)) ÷ (5 • ((2)(-8)•(5)(-8)))
   10

Step  2  :

Raising to a Power :

 2.1    5¹   divided by   5⁸   = 5^{(1 - 8)} = 5^(-7) = ¹/_5⁷

Equation at the end of step  2  :

   35                1   
  (—— • (10-4)) ÷ ———————
   10             (28•57)

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

   35                           1   
  (—— • ((2)(-4)•(5)(-4))) ÷ ———————
   10                        (28•57)

Step  4  :

            7
 Simplify   —
            2

Equation at the end of step  4  :

  7                           1   
  — • ((2)(-4)•(5)(-4))) ÷ ———————
  2                        (28•57)

Step  5  :

Multiplying exponents :

 5.1    2¹  multiplied by  2⁴   = 2^{(1 + 4)} = 2⁵

Equation at the end of step  5  :

     7         1   
  ——————— ÷ ———————
  (25•54)   (28•57)

Step  6  :

            7            1   
 Divide  ———————  by  ———————
         (25•54)      (28•57)

 6.1    Dividing fractions

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

   7           1             7        (28•57)
———————  ÷  ———————   =   ———————  •  ———————
(25•54)     (28•57)       (25•54)        1   

Dividing exponents :

 6.2    2⁸   divided by   2⁵   = 2^{(8 - 5)} = 2³

Dividing exponents :

 6.3    5⁷   divided by   5⁴   = 5^{(7 - 4)} = 5³

Final result :

  7000