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): "3.25" was replaced by "(325/100)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

  )325
  ———— • ((2)(-4)•(5)(-4)))
  (100

Step  2  :

            13
 Simplify   ——
            4 

Equation at the end of step  2  :

  13
  —— • ((2)(-4)•(5)(-4)))
  (4

Step  3  :

Raising to a Power :

 3.1    2²  multiplied by  2⁴   = 2^{(2 + 4)} = 2⁶

Equation at the end of step  3  :

  14)13 
  ———————
  (26•54)

Step  4  :

 4.1     10 = 2•5

(10)^-14 = (2•5)^(-14) = (2)^(-14) • (5)^(-14)

Equation at the end of step  4  :

  4))13 
  ———————
  (26•54)

Step  5  :

             1             13  
 Divide  —————————  by  ———————
         (214•514)       (26•54)

 5.1    Dividing fractions

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

    1            13             1         (26•54)
—————————  ÷  ———————   =   —————————  •  ———————
(214•514)      (26•54)       (214•514)        13   

Dividing exponents :

 5.2    2⁶   divided by   2¹⁴   = 2^{(6 - 14)} = 2^(-8) = ¹/_2⁸

Dividing exponents :

 5.3    5⁴   divided by   5¹⁴   = 5^{(4 - 14)} = 5^(-10) = ¹/_5¹⁰

Final result :

       1                                        
  ——————————— = 3.07692 • 10-11 
  (28•510•13)