Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4." was replaced by "(4/1)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)² = (2•5)² = 2² • 5²

Equation at the end of step  1  :

    23        4
  ((——•(107))•—)•(22•52)
    10        1

Step  2  :

            4
 Simplify   —
            1

Equation at the end of step  2  :

    23
  ((—— • (107)) • 4) • (22•52)
    10

Step  3  :

 3.1     10 = 2•5

(10)⁷ = (2•5)⁷ = 2⁷ • 5⁷

Equation at the end of step  3  :

    23
  ((—— • (27•57)) • 4) • (22•52)
    10

Step  4  :

            23
 Simplify   ——
            10

Equation at the end of step  4  :

    23
  ((—— • (27•57)) • 4) • (22•52)
    10

Step  5  :

Dividing exponents :

 5.1    2⁷   divided by   2¹   = 2^{(7 - 1)} = 2⁶

Dividing exponents :

 5.2    5⁷   divided by   5¹   = 5^{(7 - 1)} = 5⁶

Equation at the end of step  5  :

  ((23•26•56) • 4) • (22•52)

Step  6  :

Multiplying exponents :

 6.1    2⁶  multiplied by  2²   = 2^{(6 + 2)} = 2⁸

Equation at the end of step  6  :

  (23•28•56) • (22•52)

Step  7  :

Multiplying exponents :

 7.1    2⁸  multiplied by  2²   = 2^{(8 + 2)} = 2¹⁰

Multiplying exponents :

 7.2    5⁶  multiplied by  5²   = 5^{(6 + 2)} = 5⁸

Final result :

  (23•210•58)