Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.5" was replaced by "(15/10)". 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  :

   45 15
  (——•——)•(212•512)
   10 10

Step  2  :

            3
 Simplify   —
            2

Equation at the end of step  2  :

   45   3
  (—— • —) • (212•512)
   10   2

Step  3  :

 3.1     10 = 2•5

(10)³⁶ = (2•5)³⁶ = 2³⁶ • 5³⁶

Equation at the end of step  3  :

   45   3
  (—— • —) • (212•512)
   10   2

Step  4  :

                        3
 Divide  (236•536)  by  —
                        2

Multiplying exponents :

 4.1    2³⁶  multiplied by  2¹   = 2^{(36 + 1)} = 2³⁷

Equation at the end of step  4  :

   45   (237•536) 
  (—— • —————————) • (212•512)
   10       3    

Step  5  :

            9
 Simplify   —
            2

Equation at the end of step  5  :

   9   (237•536) 
  (— • —————————) • (212•512)
   2       3    

Step  6  :

Dividing exponents :

 6.1    3²   divided by   3¹   = 3^{(2 - 1)} = 3¹ = 3

Dividing exponents :

 6.2    2³⁷   divided by   2¹   = 2^{(37 - 1)} = 2³⁶

Equation at the end of step  6  :

  (3•236•536) • (212•512)

Step  7  :

Multiplying exponents :

 7.1    2³⁶  multiplied by  2¹²   = 2^{(36 + 12)} = 2⁴⁸

Multiplying exponents :

 7.2    5³⁶  multiplied by  5¹²   = 5^{(36 + 12)} = 5⁴⁸

Final result :

  (3•248•548)