Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "4.1" was replaced by "(41/10)". 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  :

    31        41
  ((——•(105))•——)•(27•57)
    10        10

Step  2  :

            41
 Simplify   ——
            10

Equation at the end of step  2  :

    31            41
  ((—— • (105)) • ——) • (27•57)
    10            10

Step  3  :

 3.1     10 = 2•5

(10)⁵ = (2•5)⁵ = 2⁵ • 5⁵

Equation at the end of step  3  :

    31              41
  ((—— • (25•55)) • ——) • (27•57)
    10              10

Step  4  :

            31
 Simplify   ——
            10

Equation at the end of step  4  :

    31              41
  ((—— • (25•55)) • ——) • (27•57)
    10              10

Step  5  :

Dividing exponents :

 5.1    2⁵   divided by   2¹   = 2^{(5 - 1)} = 2⁴

Dividing exponents :

 5.2    5⁵   divided by   5¹   = 5^{(5 - 1)} = 5⁴

Equation at the end of step  5  :

                41
  ((31•24•54) • ——) • (27•57)
                10

Step  6  :

Dividing exponents :

 6.1    2⁴   divided by   2¹   = 2^{(4 - 1)} = 2³

Dividing exponents :

 6.2    5⁴   divided by   5¹   = 5^{(4 - 1)} = 5³

Equation at the end of step  6  :

  (31•23•53•41) • (27•57)

Step  7  :

Multiplying exponents :

 7.1    2³  multiplied by  2⁷   = 2^{(3 + 7)} = 2¹⁰

Multiplying exponents :

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

Final result :

  (31•210•510•41)