Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.6" was replaced by "(46/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  1  :

   23        46
  (——•(1012))——•(23•53))
   10(       10

Step  2  :

            23
 Simplify   ——
            5 

Equation at the end of step  2  :

   23              23
  (—— • (1012)) ÷ (—— • (23•53))
   10              5 

Step  3  :

Raising to a Power :

 3.1    5³   divided by   5¹   = 5^{(3 - 1)} = 5²

Equation at the end of step  3  :

   23
  (—— • (1012)) ÷ 4600
   10

Step  4  :

 4.1     10 = 2•5

(10)¹² = (2•5)¹² = 2¹² • 5¹²

Equation at the end of step  4  :

   23
  (—— • (212•512)) ÷ 4600
   10

Step  5  :

            23
 Simplify   ——
            10

Equation at the end of step  5  :

  23
  —— • (212•512)) ÷ 4600
  10

Step  6  :

Dividing exponents :

 6.1    2¹²   divided by   2¹   = 2^{(12 - 1)} = 2¹¹

Dividing exponents :

 6.2    5¹²   divided by   5¹   = 5^{(12 - 1)} = 5¹¹

Equation at the end of step  6  :

Step  7  :

            (23•211•511) 
 Simplify   ————————————
                4600    

Canceling Out :

 7.1      Canceling out  23  as it appears on both sides of the fraction line

Dividing exponents :

 7.2    2¹¹   divided by   2³   = 2^{(11 - 3)} = 2⁸

Dividing exponents :

 7.3    5¹¹   divided by   5²   = 5^{(11 - 2)} = 5⁹

Final result :

  (28•59)