Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "8.17" was replaced by "(817/100)". 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  :

   205         817
  (———•(105))•(———•(23•53))
   100         100

Step  2  :

            817
 Simplify   ———
            100

Equation at the end of step  2  :

   205             817
  (——— • (105)) • (——— • (23•53))
   100             100

Step  3  :

Dividing exponents :

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

Raising to a Power :

 3.2    5³   divided by   5²   = 5^{(3 - 2)} = 5¹ = 5

Equation at the end of step  3  :

   205
  (——— • (105)) • 8170
   100

Step  4  :

 4.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  4  :

   205
  (——— • (25•55)) • 8170
   100

Step  5  :

            41
 Simplify   ——
            20

Equation at the end of step  5  :

   41
  (—— • (25•55)) • 8170
   20

Step  6  :

Dividing exponents :

 6.1    2⁵   divided by   2²   = 2^{(5 - 2)} = 2³

Dividing exponents :

 6.2    5⁵   divided by   5¹   = 5^{(5 - 1)} = 5⁴

Equation at the end of step  6  :

  (41•23•54) • 8170

Step  7  :

Multiplying exponents :

 7.1    2³  multiplied by  2¹   = 2^{(3 + 1)} = 2⁴

Multiplying exponents :

 7.2    5⁴  multiplied by  5¹   = 5^{(4 + 1)} = 5⁵

Final result :

  (41•24•55•19•43)