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)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

  (6 • (10-5)) • (5 • ((2)(-3)•(5)(-3)))

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  :

                  1 
  (6 • (10-5)) • ———
                 200

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

                             1 
  (6 • ((2)(-5)•(5)(-5))) • ———
                            200

Step  4  :

Dividing exponents :

 4.1    2¹   divided by   2⁵   = 2^{(1 - 5)} = 2^(-4) = ¹/_2⁴

Equation at the end of step  4  :

     3       1 
  ——————— • ———
  (24•55)   200

Step  5  :

Multiplying exponents :

 5.1    2⁴  multiplied by  2³   = 2^{(4 + 3)} = 2⁷

Multiplying exponents :

 5.2    5⁵  multiplied by  5²   = 5^{(5 + 2)} = 5⁷

Final result :

     3                                     
  ——————— = 3.00000 • 10-7 
  (27•57)