Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-8" was replaced by "^(-8)".

(2): "8.2" was replaced by "(82/10)".

Step  1  :

 1.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  1  :

  )82
  ——— • (24•54))
  (10

Step  2  :

            41
 Simplify   ——
            5 

Equation at the end of step  2  :

  41
  —— • (24•54))
  (5

Step  3  :

Raising to a Power :

 3.1    5⁴   divided by   5¹   = 5^{(4 - 1)} = 5³

Equation at the end of step  3  :

Step  4  :

 4.1     10 = 2•5

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

Equation at the end of step  4  :

Step  5  :

Dividing exponents :

 5.1    2²   divided by   2⁸   = 2^{(2 - 8)} = 2^(-6) = ¹/_2⁶

Equation at the end of step  5  :

     1   
  ——————— ÷ (41•24•53)
  (26•58)

Step  6  :

            1         
 Divide  ———————  by  (41•24•53)
         (26•58)      

Multiplying exponents :

 6.1    2⁶  multiplied by  2⁴   = 2^{(6 + 4)} = 2¹⁰

Multiplying exponents :

 6.2    5⁸  multiplied by  5³   = 5^{(8 + 3)} = 5¹¹

Final result :

        1                                        
  ———————————— = 4.87805 • 10-13 
  (210•511•41)