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  :

        (10-8)
  (15 • ——————) • ((2)(-3)•(5)(-3))
          6   

Step  2  :

 2.1     10 = 2•5

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

Equation at the end of step  2  :

        ((2)(-8)•(5)(-8)) 
  (15 • —————————————————) • ((2)(-3)•(5)(-3))
                6        

Step  3  :

            1         
 Divide  ———————  by  6
         (28•58)      

Multiplying exponents :

 3.1    2⁸  multiplied by  2¹   = 2^{(8 + 1)} = 2⁹

Equation at the end of step  3  :

            1    
  (15 • —————————) • ((2)(-3)•(5)(-3))
        (29•58•3)

Step  4  :

Canceling Out :

 4.1      Canceling out  3  as it appears on both sides of the fraction line

Dividing exponents :

 4.2    5¹   divided by   5⁸   = 5^{(1 - 8)} = 5^(-7) = ¹/_5⁷

Equation at the end of step  4  :

     1   
  ——————— • ((2)(-3)•(5)(-3))
  (29•57)

Step  5  :

Multiplying exponents :

 5.1    2⁹  multiplied by  2³   = 2^{(9 + 3)} = 2¹²

Multiplying exponents :

 5.2    5⁷  multiplied by  5³   = 5^{(7 + 3)} = 5¹⁰

Final result :

      1                                       
  ————————— = 2.50000 • 10-11 
  (212•510)