Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.5" was replaced by "(25/10)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  1  :

   12       25
  (——•(108))——•(24•54))
   10(      10

Step  2  :

            5
 Simplify   —
            2

Equation at the end of step  2  :

   12             5
  (—— • (108)) ÷ (— • (24•54))
   10             2

Step  3  :

Multiplying exponents :

 3.1    5¹  multiplied by  5⁴   = 5^{(1 + 4)} = 5⁵

Raising to a Power :

 3.2    2⁴   divided by   2¹   = 2^{(4 - 1)} = 2³

Equation at the end of step  3  :

   12
  (—— • (108)) ÷ (55•23)
   10

Step  4  :

 4.1     10 = 2•5

(10)⁸ = (2•5)⁸ = 2⁸ • 5⁸

Equation at the end of step  4  :

   12
  (—— • (28•58)) ÷ (55•23)
   10

Step  5  :

            6
 Simplify   —
            5

Equation at the end of step  5  :

  6
  — • (28•58)) ÷ (55•23)
  5

Step  6  :

Multiplying exponents :

 6.1    2¹  multiplied by  2⁸   = 2^{(1 + 8)} = 2⁹

Dividing exponents :

 6.2    5⁸   divided by   5¹   = 5^{(8 - 1)} = 5⁷

Equation at the end of step  6  :

Step  7  :

            (29•3•57)
 Simplify   —————————
             (55•23) 

Dividing exponents :

 7.1    2⁹   divided by   2³   = 2^{(9 - 3)} = 2⁶

Dividing exponents :

 7.2    5⁷   divided by   5⁵   = 5^{(7 - 5)} = 5²

Final result :

  4800