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)³ = (2•5)³ = 2³ • 5³

Equation at the end of step  1  :

   78       15
  (——•(104))——•(23•53))
   10(      10

Step  2  :

            3
 Simplify   —
            2

Equation at the end of step  2  :

   78             3
  (—— • (104)) ÷ (— • (23•53))
   10             2

Step  3  :

Raising to a Power :

 3.1    2³   divided by   2¹   = 2^{(3 - 1)} = 2²

Equation at the end of step  3  :

   78
  (—— • (104)) ÷ 1500
   10

Step  4  :

 4.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  4  :

   78
  (—— • (24•54)) ÷ 1500
   10

Step  5  :

            39
 Simplify   ——
            5 

Equation at the end of step  5  :

  39
  —— • (24•54)) ÷ 1500
  5 

Step  6  :

Dividing exponents :

 6.1    5⁴   divided by   5¹   = 5^{(4 - 1)} = 5³

Equation at the end of step  6  :

Step  7  :

            (3•13•24•53)
 Simplify   ————————————
                1500    

Canceling Out :

 7.1      Canceling out  3  as it appears on both sides of the fraction line

Dividing exponents :

 7.2    2⁴   divided by   2²   = 2^{(4 - 2)} = 2²

Canceling Out :

 7.3      Canceling out  5³ as it appears on both sides of the fraction line

Final result :

  52