Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "1.26" was replaced by "(126/100)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)²¹ = (2•5)²¹ = 2²¹ • 5²¹

Equation at the end of step  1  :

    3346         126
  ((————•(1026))•———)•(221•521)
    1000         100

Step  2  :

            63
 Simplify   ——
            50

Equation at the end of step  2  :

    3346             63
  ((———— • (1026)) • ——) • (221•521)
    1000             50

Step  3  :

 3.1     10 = 2•5

(10)²⁶ = (2•5)²⁶ = 2²⁶ • 5²⁶

Equation at the end of step  3  :

    3346                63
  ((———— • (226•526)) • ——) • (221•521)
    1000                50

Step  4  :

            1673
 Simplify   ————
            500 

Equation at the end of step  4  :

    1673                63
  ((———— • (226•526)) • ——) • (221•521)
    500                 50

Step  5  :

Dividing exponents :

 5.1    2²⁶   divided by   2²   = 2^{(26 - 2)} = 2²⁴

Dividing exponents :

 5.2    5²⁶   divided by   5³   = 5^{(26 - 3)} = 5²³

Equation at the end of step  5  :

                     63
  ((7•239•224•523) • ——) • (221•521)
                     50

Step  6  :

Multiplying exponents :

 6.1    7¹  multiplied by  7¹   = 7^{(1 + 1)} = 7²

Dividing exponents :

 6.2    2²⁴   divided by   2¹   = 2^{(24 - 1)} = 2²³

Dividing exponents :

 6.3    5²³   divided by   5²   = 5^{(23 - 2)} = 5²¹

Equation at the end of step  6  :

  (72•239•223•521•32) • (221•521)

Step  7  :

Multiplying exponents :

 7.1    2²³  multiplied by  2²¹   = 2^{(23 + 21)} = 2⁴⁴

Multiplying exponents :

 7.2    5²¹  multiplied by  5²¹   = 5^{(21 + 21)} = 5⁴²

Final result :

  (72•239•244•542•32)