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)

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

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

Step  2  :

Equation at the end of step  2  :

                    7   
  (2 • (10-5)) • ———————
                 (25•55)

Step  3  :

 3.1     10 = 2•5

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

Equation at the end of step  3  :

                               7   
  (2 • ((2)(-5)•(5)(-5))) • ———————
                            (25•55)

Step  4  :

Dividing exponents :

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

Equation at the end of step  4  :

     1         7   
  ——————— • ———————
  (24•55)   (25•55)

Step  5  :

Multiplying exponents :

 5.1    2⁴  multiplied by  2⁵   = 2^{(4 + 5)} = 2⁹

Multiplying exponents :

 5.2    5⁵  multiplied by  5⁵   = 5^{(5 + 5)} = 5¹⁰

Final result :

      7                                     
  ———————— = 1.40000 • 10-9 
  (29•510)