Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-6" was replaced by "^(-6)". 1 more similar replacement(s)

(2): "3.85" was replaced by "(385/100)".

Step  1  :

 1.1     10 = 2•5

(10)^-6 = (2•5)^(-6) = (2)^(-6) • (5)^(-6)

Equation at the end of step  1  :

  385
  ——— • ((2)(-6)•(5)(-6))
  100

Step  2  :

            77
 Simplify   ——
            20

Equation at the end of step  2  :

  77
  —— • ((2)(-6)•(5)(-6))
  20

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

  77
  —— • ((2)(-6)•(5)(-6))
  20

Step  4  :

            1         77
 Divide  ———————  by  ——
         (23•53)      20

 4.1    Dividing fractions

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

   1        77          1        20
———————  ÷  ——   =   ———————  •  ——
(23•53)     20       (23•53)     77

Dividing exponents :

 4.2    2²   divided by   2³   = 2^{(2 - 3)} = 2^(-1) = ¹/_2¹ = ¹/₂

Dividing exponents :

 4.3    5¹   divided by   5³   = 5^{(1 - 3)} = 5^(-2) = ¹/_5²

Equation at the end of step  4  :

    1 
  ———— • ((2)(-6)•(5)(-6))
  3850

Step  5  :

Multiplying exponents :

 5.1    2¹  multiplied by  2⁶   = 2^{(1 + 6)} = 2⁷

Multiplying exponents :

 5.2    5²  multiplied by  5⁶   = 5^{(2 + 6)} = 5⁸

Final result :

        1                                        
  ———————————— = 2.59740 • 10-10 
  (27•58•7•11)