Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "8.65" was replaced by "(865/100)". 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  :

   602          865
  (———•(1023))•(———•(24•54))
   100          100

Step  2  :

            173
 Simplify   ———
            20 

Equation at the end of step  2  :

   602              173
  (——— • (1023)) • (——— • (24•54))
   100              20 

Step  3  :

Dividing exponents :

 3.1    2⁴   divided by   2²   = 2^{(4 - 2)} = 2²

Raising to a Power :

 3.2    5⁴   divided by   5¹   = 5^{(4 - 1)} = 5³

Equation at the end of step  3  :

   602
  (——— • (1023)) • (173•22•53)
   100

Step  4  :

 4.1     10 = 2•5

(10)²³ = (2•5)²³ = 2²³ • 5²³

Equation at the end of step  4  :

   602
  (——— • (223•523)) • (173•22•53)
   100

Step  5  :

            301
 Simplify   ———
            50 

Equation at the end of step  5  :

   301
  (——— • (223•523)) • (173•22•53)
   50 

Step  6  :

Dividing exponents :

 6.1    2²³   divided by   2¹   = 2^{(23 - 1)} = 2²²

Dividing exponents :

 6.2    5²³   divided by   5²   = 5^{(23 - 2)} = 5²¹

Equation at the end of step  6  :

  (7•43•222•521) • (173•22•53)

Step  7  :

Multiplying exponents :

 7.1    2²²  multiplied by  2²   = 2^{(22 + 2)} = 2²⁴

Multiplying exponents :

 7.2    5²¹  multiplied by  5³   = 5^{(21 + 3)} = 5²⁴

Final result :

  (7•43•224•524•173)