Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "3.3" was replaced by "(33/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)¹² = (2•5)¹² = 2¹² • 5¹²

Equation at the end of step  1  :

   891         33
  (———•(102))•(——•(212•512))
   100         10

Step  2  :

            33
 Simplify   ——
            10

Equation at the end of step  2  :

   891             33
  (——— • (102)) • (—— • (212•512))
   100             10

Step  3  :

Dividing exponents :

 3.1    2¹²   divided by   2¹   = 2^{(12 - 1)} = 2¹¹

Raising to a Power :

 3.2    5¹²   divided by   5¹   = 5^{(12 - 1)} = 5¹¹

Equation at the end of step  3  :

   891
  (——— • (102)) • (3•11•211•511)
   100

Step  4  :

 4.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  4  :

   891
  (——— • (22•52)) • (3•11•211•511)
   100

Step  5  :

            891
 Simplify   ———
            100

Equation at the end of step  5  :

   891
  (——— • (22•52)) • (3•11•211•511)
   100

Step  6  :

Canceling Out :

 6.1      Canceling out  2² as it appears on both sides of the fraction line

Canceling Out :

 6.2      Canceling out  5² as it appears on both sides of the fraction line

Equation at the end of step  6  :

  891 • (3•11•211•511)

Step  7  :

Multiplying exponents :

 7.1    3⁴  multiplied by  3¹   = 3^{(4 + 1)} = 3⁵

Multiplying exponents :

 7.2    11¹  multiplied by  11¹   = 11^{(1 + 1)} = 11²

Final result :

  (35•112•211•511)