Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "^-3" was replaced by "^(-3)".

(2): "2.2" was replaced by "(22/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)^-3 = (2•5)^(-3) = (2)^(-3) • (5)^(-3)

Equation at the end of step  1  :

   88       22
  (——•(109))——•((2)(-3)•(5)(-3)))
   10(      10

Step  2  :

            11
 Simplify   ——
            5 

Equation at the end of step  2  :

   88             11
  (—— • (109)) ÷ (—— • ((2)(-3)•(5)(-3)))
   10             5 

Step  3  :

Raising to a Power :

 3.1    5¹  multiplied by  5³   = 5^{(1 + 3)} = 5⁴

Equation at the end of step  3  :

   88             11 
  (—— • (109)) ÷ ————
   10            5000

Step  4  :

 4.1     10 = 2•5

(10)⁹ = (2•5)⁹ = 2⁹ • 5⁹

Equation at the end of step  4  :

   88               11 
  (—— • (29•59)) ÷ ————
   10              5000

Step  5  :

            44
 Simplify   ——
            5 

Equation at the end of step  5  :

  44               11 
  —— • (29•59)) ÷ ————
  5               5000

Step  6  :

Multiplying exponents :

 6.1    2²  multiplied by  2⁹   = 2^{(2 + 9)} = 2¹¹

Dividing exponents :

 6.2    5⁹   divided by   5¹   = 5^{(9 - 1)} = 5⁸

Equation at the end of step  6  :

  )11 
  ————
  5000

Step  7  :

                           11 
 Divide  (211•11•58)  by  ————
                          5000

Multiplying exponents :

 7.1    2¹¹  multiplied by  2³   = 2^{(11 + 3)} = 2¹⁴

Multiplying exponents :

 7.2    5⁸  multiplied by  5⁴   = 5^{(8 + 4)} = 5¹²

Canceling Out :

 7.3      Canceling out  11  as it appears on both sides of the fraction line

Final result :

  (214•512)