Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-5" was replaced by "^(-5)".

(2): "4.4" was replaced by "(44/10)".

Step  1  :

 1.1     10 = 2•5

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

Equation at the end of step  1  :

   44
  (—— • (108)) ÷ (2 • ((2)(-5)•(5)(-5)))
   10

Step  2  :

Raising to a Power :

 2.1    2¹   divided by   2⁵   = 2^{(1 - 5)} = 2^(-4) = ¹/_2⁴

Equation at the end of step  2  :

   44               1   
  (—— • (108)) ÷ ———————
   10            (24•55)

Step  3  :

 3.1     10 = 2•5

(10)⁸ = (2•5)⁸ = 2⁸ • 5⁸

Equation at the end of step  3  :

   44                 1   
  (—— • (28•58)) ÷ ———————
   10              (24•55)

Step  4  :

            22
 Simplify   ——
            5 

Equation at the end of step  4  :

  22                 1   
  —— • (28•58)) ÷ ———————
  5               (24•55)

Step  5  :

Multiplying exponents :

 5.1    2¹  multiplied by  2⁸   = 2^{(1 + 8)} = 2⁹

Dividing exponents :

 5.2    5⁸   divided by   5¹   = 5^{(8 - 1)} = 5⁷

Equation at the end of step  5  :

  7)1 
  ———————
  (24•55)

Step  6  :

                            1   
 Divide  (29•11•57)  by  ———————
                         (24•55)

Multiplying exponents :

 6.1    2⁹  multiplied by  2⁴   = 2^{(9 + 4)} = 2¹³

Multiplying exponents :

 6.2    5⁷  multiplied by  5⁵   = 5^{(7 + 5)} = 5¹²

Final result :

  (213•11•512)