Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

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

(2): "8.82" was replaced by "(882/100)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   882
  (——— • (103)) ÷ (5 • ((2)(-8)•(5)(-8)))
   100

Step  2  :

Raising to a Power :

 2.1    5¹   divided by   5⁸   = 5^{(1 - 8)} = 5^(-7) = ¹/_5⁷

Equation at the end of step  2  :

   882               1   
  (——— • (103)) ÷ ———————
   100            (28•57)

Step  3  :

 3.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  3  :

   882                 1   
  (——— • (23•53)) ÷ ———————
   100              (28•57)

Step  4  :

            441
 Simplify   ———
            50 

Equation at the end of step  4  :

  441                 1   
  ——— • (23•53)) ÷ ———————
  50               (28•57)

Step  5  :

Dividing exponents :

 5.1    2³   divided by   2¹   = 2^{(3 - 1)} = 2²

Dividing exponents :

 5.2    5³   divided by   5²   = 5^{(3 - 2)} = 5¹ = 5

Equation at the end of step  5  :

  88201  
  ———————
  (28•57)

Step  6  :

                      1   
 Divide  8820  by  ———————
                   (28•57)

Multiplying exponents :

 6.1    2²  multiplied by  2⁸   = 2^{(2 + 8)} = 2¹⁰

Multiplying exponents :

 6.2    5¹  multiplied by  5⁷   = 5^{(1 + 7)} = 5⁸

Final result :

  (210•32•58•72)