Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "3." was replaced by "(3/1)". 2 more similar replacement(s)

Step  1  :

 1.1     10 = 2•5

(10)⁷ = (2•5)⁷ = 2⁷ • 5⁷

Equation at the end of step  1  :

    32        3
  ((——•(104))•—)•(27•57)
    10        1

Step  2  :

            3
 Simplify   —
            1

Equation at the end of step  2  :

    32
  ((—— • (104)) • 3) • (27•57)
    10

Step  3  :

 3.1     10 = 2•5

(10)⁴ = (2•5)⁴ = 2⁴ • 5⁴

Equation at the end of step  3  :

    32
  ((—— • (24•54)) • 3) • (27•57)
    10

Step  4  :

            16
 Simplify   ——
            5 

Equation at the end of step  4  :

    16
  ((—— • (24•54)) • 3) • (27•57)
    5 

Step  5  :

Multiplying exponents :

 5.1    2⁴  multiplied by  2⁴   = 2^{(4 + 4)} = 2⁸

Dividing exponents :

 5.2    5⁴   divided by   5¹   = 5^{(4 - 1)} = 5³

Equation at the end of step  5  :

  ((28•53) • 3) • (27•57)

Step  6  :

Equation at the end of step  6  :

  (28•53•3) • (27•57)

Step  7  :

Multiplying exponents :

 7.1    2⁸  multiplied by  2⁷   = 2^{(8 + 7)} = 2¹⁵

Multiplying exponents :

 7.2    5³  multiplied by  5⁷   = 5^{(3 + 7)} = 5¹⁰

Final result :

  (215•510•3)