Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.1" was replaced by "(21/10)".

Step  1  :

 1.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  1  :

    21
  ((—— • (104)) • 4) • (25•55)
    10

Step  2  :

 2.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  2  :

    21
  ((—— • (24•54)) • 4) • (25•55)
    10

Step  3  :

            21
 Simplify   ——
            10

Equation at the end of step  3  :

    21
  ((—— • (24•54)) • 4) • (25•55)
    10

Step  4  :

Dividing exponents :

 4.1    2⁴   divided by   2¹   = 2^{(4 - 1)} = 2³

Dividing exponents :

 4.2    5⁴   divided by   5¹   = 5^{(4 - 1)} = 5³

Equation at the end of step  4  :

  ((3•7•23•53) • 4) • (25•55)

Step  5  :

Multiplying exponents :

 5.1    2³  multiplied by  2²   = 2^{(3 + 2)} = 2⁵

Equation at the end of step  5  :

  (3•7•25•53) • (25•55)

Step  6  :

Multiplying exponents :

 6.1    2⁵  multiplied by  2⁵   = 2^{(5 + 5)} = 2¹⁰

Multiplying exponents :

 6.2    5³  multiplied by  5⁵   = 5^{(3 + 5)} = 5⁸

Final result :

  (3•7•210•58)