Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.8" was replaced by "(18/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)⁴⁵ = (2•5)⁴⁵ = 2⁴⁵ • 5⁴⁵

Equation at the end of step  1  :

   75          18
  (——•(1040))•(——•(245•545))
   10          10

Step  2  :

            9
 Simplify   —
            5

Equation at the end of step  2  :

   75              9
  (—— • (1040)) • (— • (245•545))
   10              5

Step  3  :

Raising to a Power :

 3.1    5⁴⁵   divided by   5¹   = 5^{(45 - 1)} = 5⁴⁴

Equation at the end of step  3  :

   75
  (—— • (1040)) • (32•245•544)
   10

Step  4  :

 4.1     10 = 2•5

(10)⁴⁰ = (2•5)⁴⁰ = 2⁴⁰ • 5⁴⁰

Equation at the end of step  4  :

   75
  (—— • (240•540)) • (32•245•544)
   10

Step  5  :

            15
 Simplify   ——
            2 

Equation at the end of step  5  :

   15
  (—— • (240•540)) • (32•245•544)
   2 

Step  6  :

Multiplying exponents :

 6.1    5¹  multiplied by  5⁴⁰   = 5^{(1 + 40)} = 5⁴¹

Dividing exponents :

 6.2    2⁴⁰   divided by   2¹   = 2^{(40 - 1)} = 2³⁹

Equation at the end of step  6  :

  (3•541•239) • (32•245•544)

Step  7  :

Multiplying exponents :

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

Multiplying exponents :

 7.2    5⁴¹  multiplied by  5⁴⁴   = 5^{(41 + 44)} = 5⁸⁵

Multiplying exponents :

 7.3    2³⁹  multiplied by  2⁴⁵   = 2^{(39 + 45)} = 2⁸⁴

Final result :

  (33•585•284)