Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "6.41" was replaced by "(641/100)". 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  :

    22        641
  ((——•(104))•———)•(23•53)
    10        100

Step  2  :

            641
 Simplify   ———
            100

Equation at the end of step  2  :

    22            641
  ((—— • (104)) • ———) • (23•53)
    10            100

Step  3  :

 3.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  3  :

    22              641
  ((—— • (24•54)) • ———) • (23•53)
    10              100

Step  4  :

            11
 Simplify   ——
            5 

Equation at the end of step  4  :

    11              641
  ((—— • (24•54)) • ———) • (23•53)
    5               100

Step  5  :

Dividing exponents :

 5.1    5⁴   divided by   5¹   = 5^{(4 - 1)} = 5³

Equation at the end of step  5  :

                641
  ((11•24•53) • ———) • (23•53)
                100

Step  6  :

Dividing exponents :

 6.1    2⁴   divided by   2²   = 2^{(4 - 2)} = 2²

Dividing exponents :

 6.2    5³   divided by   5²   = 5^{(3 - 2)} = 5¹ = 5

Equation at the end of step  6  :

  (11•22•5•641) • (23•53)

Step  7  :

Multiplying exponents :

 7.1    2²  multiplied by  2³   = 2^{(2 + 3)} = 2⁵

Multiplying exponents :

 7.2    5¹  multiplied by  5³   = 5^{(1 + 3)} = 5⁴

Final result :

  (11•25•54•641)