Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "3." was replaced by "(3/1)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)¹⁸ = (2•5)¹⁸ = 2¹⁸ • 5¹⁸

Equation at the end of step  1  :

   45          3
  (——•(1016))•(—•(218•518))
   10          1

Step  2  :

            3
 Simplify   —
            1

Equation at the end of step  2  :

   45
  (—— • (1016)) • (3 • (218•518))
   10

Step  3  :

Equation at the end of step  3  :

   45
  (—— • (1016)) • (3•218•518)
   10

Step  4  :

 4.1     10 = 2•5

(10)¹⁶ = (2•5)¹⁶ = 2¹⁶ • 5¹⁶

Equation at the end of step  4  :

   45
  (—— • (216•516)) • (3•218•518)
   10

Step  5  :

            9
 Simplify   —
            2

Equation at the end of step  5  :

   9
  (— • (216•516)) • (3•218•518)
   2

Step  6  :

Dividing exponents :

 6.1    2¹⁶   divided by   2¹   = 2^{(16 - 1)} = 2¹⁵

Equation at the end of step  6  :

  (32•215•516) • (3•218•518)

Step  7  :

Multiplying exponents :

 7.1    3²  multiplied by  3¹   = 3^{(2 + 1)} = 3³

Multiplying exponents :

 7.2    2¹⁵  multiplied by  2¹⁸   = 2^{(15 + 18)} = 2³³

Multiplying exponents :

 7.3    5¹⁶  multiplied by  5¹⁸   = 5^{(16 + 18)} = 5³⁴

Final result :

  (33•233•534)