Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-4" was replaced by "^(-4)". 1 more similar replacement(s)

(2): "7.5" was replaced by "(75/10)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   75   (10-6)
  (—— • ——————) • ((2)(-4)•(5)(-4))
   10     3   

Step  2  :

 2.1     10 = 2•5

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

Equation at the end of step  2  :

   75   ((2)(-6)•(5)(-6)) 
  (—— • —————————————————) • ((2)(-4)•(5)(-4))
   10           3        

Step  3  :

            1         
 Divide  ———————  by  3
         (26•56)      

Equation at the end of step  3  :

   75       1    
  (—— • —————————) • ((2)(-4)•(5)(-4))
   10   (26•56•3)

Step  4  :

            15
 Simplify   ——
            2 

Equation at the end of step  4  :

   15       1    
  (—— • —————————) • ((2)(-4)•(5)(-4))
   2    (26•56•3)

Step  5  :

Multiplying exponents :

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

Canceling Out :

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

Dividing exponents :

 5.3    5¹   divided by   5⁶   = 5^{(1 - 6)} = 5^(-5) = ¹/_5⁵

Equation at the end of step  5  :

     1   
  ——————— • ((2)(-4)•(5)(-4))
  (27•55)

Step  6  :

Multiplying exponents :

 6.1    2⁷  multiplied by  2⁴   = 2^{(7 + 4)} = 2¹¹

Multiplying exponents :

 6.2    5⁵  multiplied by  5⁴   = 5^{(5 + 4)} = 5⁹

Final result :

      1                                      
  ———————— = 2.50000 • 10-10 
  (211•59)